Correlation of thread intensity and heap usage to identify heap-hoarding stack traces

ABSTRACT

Embodiments identify heap-hoarding stack traces to optimize memory efficiency. Some embodiments can determine a length of time when heap usage by processes exceeds a threshold. Some embodiments may then determine heap information of the processes for the length of time, where the heap information comprise heap usage information for each interval in the length of time. Next, some embodiments can determine thread information of the one or more processes for the length of time, wherein determining the thread information comprises determining classes of threads and wherein the thread information comprises, for each of the classes of threads, thread intensity information for each of the intervals. Some embodiments may then correlate the heap information with the thread information to identify code that correspond to the heap usage exceeding the threshold. Some embodiments may then initiate actions associated with the code.

CROSS-REFERENCES TO RELATED APPLICATIONS

The present application is a continuation of U.S. Non-Provisionalapplication Ser. No. 15/588,531, filed May 5, 2017, entitled“Correlation of Thread Intensity and Heap Usage to IdentifyHeap-Hoarding Stack Traces,” which is a non-provisional of and claimsthe benefit and priority under 35 U.S.C. 119(e) of U.S. ProvisionalApplication No. 62/333,786, filed May 9, 2016, entitled “Correlation ofThread Intensity and Heap Usage to Identify Heap-Hoarding Stack Traces,”U.S. Provisional Application No. 62/333,798, filed May 9, 2016, entitled“Memory Usage Determination Techniques,” U.S. Provisional ApplicationNo. 62/333,804, filed May 9, 2016, entitled “Compression Techniques forEncoding Stack Traces Information,” U.S. Provisional Application No.62/333,811, filed May 9, 2016, entitled “Correlation of Stack SegmentIntensity in Emergent Relationships,” U.S. Provisional Application No.62/333,809, filed May 9, 2016, entitled “Systems and Methods of StackTrace Analysis,” and U.S. Provisional Application No. 62/340,256, filedMay 23, 2016, entitled “Characterization of Segments of Time-Series,”the entire contents of which are incorporated herein by reference forall purposes.

The present application is related to the following concurrently filedapplications, the entire contents of which are incorporated herein byreference for all purposes:

(1) U.S. Non-Provisional application Ser. No. 15/588,526, entitled“MEMORY USAGE DETERMINATION TECHNIQUES” filed May 5, 2017.

(2) U.S. Non-Provisional application Ser. No. 15/588,523, entitled“COMPRESSION TECHNIQUES FOR ENCODING STACK TRACE INFORMATION” filed May5, 2017.

(3) U.S. Non-Provisional application Ser. No. 15/588,521, entitled“CORRELATION OF STACK SEGMENT INTENSITY IN EMERGENT RELATIONSHIPS” filedMay 5, 2017.

BACKGROUND

In general, cloud service providers maintain operational resources tomeet service level agreements (SLA) with customers. The providerscontinuously monitor the performance metrics of the cloud services theyprovide to ensure the services' conformance to SLAs. However, becauseavailable tools may lack the capability to predict or detect impendingSLA violations, the operational resources may be unable to circumventthe violations. Additionally, because the tools may lack the capabilityto diagnosis the root causes of SLA violations, the operations may takelonger to resolve such violations when they do occur. As a result, thecustomer experience may be adversely affected.

Furthermore, such SLAs might require that data be analyzedsystematically and actionable information in the data be acted uponproactively to avoid SLA violations and also to determine whether theagreement is being satisfied. Following the service level agreements andother requirements can be very burdensome, and can grow more burdensomewith the passage of time.

For obtaining the capabilities mentioned above, what is needed aretechniques that represent the system using high-level state models thatare easily updated based on low-level events of the system and systemmeasurements. With regards to obtaining metrics on low-level events, onecan instrument application programs underlying the system to collect theexact measurements of the events. In such an approach, however, theinstrumentation itself can affect the measurements. This problem can bemore pronounced when the execution time of the instrumentation codearound a method dominates the execution time of the method itself (e.g.,if the invocation count of the method is high).

BRIEF SUMMARY

Certain techniques are disclosed for identifying heap-hoarding stacktraces to optimize memory efficiency. Some embodiments may correlateheap information with the thread information to identify code thatcorresponds to high heap usage within a software execution environment.

One embodiment is directed to a method. The method can include:determining, by one or more computer systems, a length of time when heapusage by one or more processes exceeds a threshold; determining heapinformation of the one or more processes for the length of time, theheap information comprising heap usage information for each of aplurality of intervals in the length of time; determining threadinformation of the one or more processes for the length of time, whereindetermining the thread information comprises determining one or moreclasses of threads and wherein the thread information comprises, foreach of the one or more classes of threads, thread intensity informationfor each of the plurality of intervals; correlating the heap informationwith the thread information to identify one or more lines of code of theone or more processes that correspond to the heap usage exceeding thethreshold; and responsive to identifying the one or more lines of code,initiating one or more actions associated with the one or more lines ofcode.

BRIEF DESCRIPTION OF THE DRAWINGS

Illustrative embodiments are described in detail below in reference tothe following drawing figures:

FIG. 1 depicts an exemplary runtime profiling of a single thread over aperiod of time at a relatively high frequency sampling rate.

FIG. 2 depicts an exemplary calling context tree.

FIG. 3 depicts exemplary thread dumps of a virtual machine over a periodof time, according to some embodiments.

FIGS. 4-6 depict exemplary thread classification signatures, accordingto some embodiments.

FIG. 7 shows a simplified flowchart that depicts the generation and/ormodification of one or more thread classification signatures in responseto a thread dump according to some embodiments.

FIG. 8 shows a simplified flowchart that depicts the generation ormodification of a thread classification signature in response todetecting a branch point.

FIG. 9 shows a simplified flowchart that depicts the identification ofcode that corresponds to high heap usage according to some embodiments.

FIG. 10 shows a simplified flowchart that depicts the calculation ofdegrees of correlation between various classes of threads and high heapusage according to some embodiments.

FIG. 11 depicts an example graph where the weight assigned to a samplemeasurement is plotted against the sampling time interval associatedwith the sample measurement across a time range of an example data set.

FIG. 12 depicts an example chart showing trend graphs derived bydifferent linear regression techniques for the heap usage in aproduction environment.

FIG. 13 depicts an example chart showing an additional trend graph thatillustrates incorrect results given by standard robust regressiontechniques.

FIG. 14 shows a simplified flowchart that depicts the generation of aforecast of a signal according to some embodiments.

FIG. 15 depicts a simplified diagram of a distributed system forimplementing certain embodiments.

FIG. 16 depicts a simplified block diagram of one or more components ofa system environment in which services may be offered as cloud services,in accordance with some embodiments.

FIG. 17 depicts an exemplary computer system that may be used toimplement certain embodiments.

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawings will be provided by the Office upon request and paymentof the necessary fee.

DETAILED DESCRIPTION

I. Overview

In the following description, for the purposes of explanation, specificdetails are set forth in order to provide a thorough understanding ofembodiments of the disclosure. However, it will be apparent that variousembodiments may be practiced without these specific details. The figuresand description are not intended to be restrictive.

The present disclosure relates generally to using heap usage statisticsand thread intensity statistics to identify code blocks within amulti-threaded process (e.g., an application program) for potentialoptimization and to forecast future heap usage and/or thread intensity.Thread intensity statistics may be used to track the response, load, andresource usage of the process without instrumenting the process'sunderlying code or using code injection. In particular, the intensity ofa thread's type or a stack segment's type may refer to a statisticalmeasure of the “hotness” of the code blocks being executed by the threador referenced by the stack segment. The hotness of a code block can bequantified by volume of execution (e.g., the number of invocations ofthe code block multiplied by the execution time of the code block).Hotter code blocks have a higher number of invocations and/or longerresponse times.

By analyzing a series of thread dumps taken from a process at regular orirregular time intervals, some embodiments may provide a statisticalsampling solution that is (1) low-overhead, (2) non-intrusive, (3)provides always-on monitoring, and (4) avoids the problem ofinstrumentation code dominating the execution time of the code beinginstrumented (i.e., the Heisenberg problem).

Some embodiments may classify threads and stack segments based onintensity statistics. By monitoring stack traces of individual threadsincluded in thread dumps received from an software execution environment(e.g., a virtual machine), a monitoring process can classify the threadsbased on the contents of their stack traces into one or more threadclasses. As more stack traces are analyzed, some embodiments may observethe bifurcation of thread classes into sub-classes and eventually builda hierarchy of thread classes. For example, if a stack segment (A) isobserved to be a component of a stack segment (A, B, D), one could saythat the thread type (A, B, D) is a sub-class of thread type (A). Onecould also say that thread type (A, C) is a sub-class of thread type(A). The thread type (A) includes sub-classes (A, B, D) and (A, C) inthe sense that the aggregate of intensity statistics corresponding to(A, B, D) and (A, C) can be represented by the intensity statisticscorresponding to (A). Additionally, some embodiments may travel (e.g.,traversing a tree or graph) down the thread class hierarchy to observehow the intensity of a particular thread class can be proportionallyattributed to the intensities of one or more sub-classes of the threadclass. For example, the thread intensity of (A) can be proportionallyattributed to the thread intensities of (A, B, D) and (A, C). In otherembodiments, each stack trace may be represented as a binary tree.

Some embodiments can provide one or more sequential filters to estimatethe measure, rate of change, acceleration, seasonal factor, andresidual. Techniques to represent separate seasonal indices for multipleperiods (e.g., a weekday period and a weekend period) and to normalizethe seasonal factors for the multiple periods may be performed by suchembodiments. In particular, some embodiments may represent a separatesequence of seasonal indices for each of the multiple periods. Forexample, the multiple periods may include a weekday period, a weekendperiod, an end-of-quarter period, or individual holiday periods. Inestimating seasonal indices for multiple periods, some embodiments mayalso (1) renormalize the seasonal indices to provide a common scale anda common reference level across all periods and (2) fit a smooth-splineacross adjacent periods to provide smooth transitions between the cyclesof a period or between the cycles of two adjacent periods. Byrenormalization, the seasonal factors across the multiple periods canhave a common scale.

Some embodiments may correlate trends between intensity statistics ofvarious classes of threads and heap usage statistics to identify classesof threads whose intensity statistics have a high degree of correlationwith high heap usage. There is a high probability of finding inefficientheap memory usage among classes of threads whose intensity statisticsare highly correlated with the high heap usage in the software executionenvironment. Once the classes of threads are identified, the codeassociated with the classes of threads may investigated and/oroptimized.

Some embodiments may construct and maintain models (e.g., univariate,multivariate) of the multi-threaded environment (e.g., virtual machine)executing the process, where the models include seasonal trends, lineartrends, and first-order non-linear trends for the intensities of eachthread class. Such models may be used to obtain seasonally adjusted longterm forecasts on the trend of the system's performance.

By (1) dynamically classifying threads and observing how the intensitiesof sub-classes of thread classes contribute to an aggregate intensity ofthe thread class and (2) observing how closely various classes ofthreads are correlated with detected periods of high heap usage, someembodiments may facilitate the detection and observation of performanceglitches within cloud service provisioning systems. Because even minorperformance glitches often reveal issues within the process that canresult in SLA violations, enabling service providers to detect andaddress performance glitches may substantially reduce the risk of suchviolations.

II. Runtime Profiling of Threads

FIGS. 1-2 depict techniques of profiling a running thread to determinehow long various stack segments are present on the thread's call stackin relation to one another. FIG. 1 depicts an exemplary runtimeprofiling of a single thread 100 over a period of time at a relativelyhigh frequency sampling rate. In some cases, certain techniques mayutilize a runtime profiler to take multiple stack trace samples of athread to construct a calling context tree 200 shown in FIG. 2. If thesampling interval employed by the runtime profiler is relatively shortcompared to the thread's execution time, the observation count (i.e.,call count) statistics for each calling context of the thread can beused to accurately estimate and/or represent the execution time of thecalling context relative to the sampling interval.

For example, as shown in FIG. 1, the total execution time of the thread100 may be between 100 milliseconds and one second while the samplinginterval is between 10 milliseconds and 100 milliseconds. During thethread's execution, different calling contexts may be present within thethread's stack depending on which methods are invoked by the thread. Thethread may begin its execution by invoking a set of methods thatcorrespond to stack segment A.

It should be noted that a stack segment corresponds to a set of one ormore stack frames that are linearly connected. Stack frames that arelinearly connected are always observed together within stack traces andthus have the same intensity statistics. Thus, stack segment A maycorrespond to a plurality of stack frames such as stack frames a1, a2,and a3. Sampling a thread may result in a stack trace that describes anentire calling context of the sampled thread in a list of stack frames.If some of the listed stack frames are linearly connected, those stackframes may be conceptually grouped into a stack segment. As a result, astack trace may include one or more stack segments, with each stacksegment including one or more stack frames.

As the thread continues its execution, code associated with stacksegment A may cause the thread to invoke a set of methods thatcorrespond to stack segment B. Next, code associated with stack segmentB may cause the thread to invoke yet another set of methods thatcorrespond to stack segment D. After a short period of time, the runtimeprofiler may take sample 1 of the thread 100, resulting in a first stacktrace. From the first stack trace, the runtime profiler may determinethat stack segments A, B, and D were on the stack at the time of thesampling. After a sampling interval, the runtime profiler may takeanother sample 2 of the thread, resulting in a second stack trace. Fromthe second stack trace, the runtime profiler may determine that stacksegments A, B, and D were on the stack. As the thread continues toexecute, the methods associated with stack segment D may return,resulting in the stack frames corresponding to stack segment D beingpopped off the stack. Next, the runtime profiler may take another sample3 of the thread, resulting in a third stack trace. From the third stacktrace, the runtime profiler may determine that stack segments A and Bwere on the stack.

As the thread executes, stack segment B invokes stack segment E, whichinvokes stack segment F. Next, taking sample 4 results in a fourth stacktrace indicating that stack segments A, B, E, and F were on the stack.Stack segments F, E, and B return one after another. Next, taking sample5 results in a fifth stack trace indicating that only stack segment A ison the stack. Stack segment A causes stack segment C to be pushed ontothe stack. Before stack segment C returns, samples 6 and 7 are taken,resulting in a sixth stack trace and a seventh stack trace that bothindicate that stack segments A and C are on the stack. Eventually, stacksegment C returns, leaving only stack segment A on the stack. When themethods associated with stack segment A return, the thread finishesexecuting.

As shown in FIG. 2, calling context tree 200 depicts the execution timesof stack segments A-F relative to the sampling interval. Node 202indicates that stack segment A was observed in all of the seven samples.Node 204 indicates that stack segment B was observed in four of theseven samples. Node 206 indicates that stack segment C was observed intwo of the seven samples. Node 208 indicates that stack segment D wasobserved in two of the seven samples. Node 210 indicates that stacksegment E was observed in one of the seven samples. Node 212 indicatesthat stack segment F was observed in one of the seven samples. Becausethe total execution time of thread 100 is approximately ten times theduration of the sampling interval, the observation count for each stacksegment may be closely correlated with the stack segment's executiontime. For example, because stack segment B was observed four times, itmay be inferred that the relative execution time of stack segment B isat least four times the sampling interval.

In some cases, the environment where the thread 100 executes (i.e., thesoftware execution environment) may correspond to a virtual machine(e.g., a Hotspot Java Virtual Machine (JVM)) where a thread dump istaken once per sampling interval. Before the virtual machine takes athread dump, it may signal all executing threads (e.g., thread 100) topause at safepoints. This safepoint mechanism may be similar to the oneused by a garbage collector to pause threads prior to executing a fullgarbage collection. Note that a thread running in kernel mode (e.g.,running/blocking on I/O operation) may not pause at a safepoint untilthe thread returns out of kernel mode (e.g., back to JVM mode).

It should be noted however, that invoking the safepoint mechanism at ahigh frequency rate may result in substantial overhead. Thus, runtimeprofiling techniques that rely on a high sampling rate may be moreappropriate for development or testing environments rather thanproduction environments.

To reduce overhead, some embodiments employ system models to compensatefor a reduced sampling rate. For example, some embodiments may track theintensities of threads of a multi-threaded process and sample onlythreads with intensities exceeding a threshold that determines latency.One advantage with embodiments that employ reduced samplings rates oradaptive samplings rates is that threads running in kernel mode are lesslikely to be paused at safepoints. Other methods of reducing overheadmay involve lengthening the sampling interval to be commensurate withthe intensity of the threads being sampled. For instance, while a oneminute sampling interval may result in negligible overhead within aproduction environment, the one minute sampling interval may be shortenough for deriving the relative execution time of threads and theircomponent stack segments in the production environment. Thus, someembodiments may provide an always-on performance monitoring solution forproduction systems that exhibit stationary mean-ergodicity orcyclo-stationary mean ergodicity for satisfying the assumptions ofLittle's formula. In such embodiments, the always-on performancemonitoring solution may be embodied in a monitoring process (i.e., acontrol system) that periodically samples threads executing within oneor more virtual machines of the production system.

III. Classifying Threads

Various embodiments provide techniques for sequentially analyzing aseries of thread dump samples taken from one or more virtual machines(e.g., JVMs) to identify thread classes and to track intensitystatistics pertaining to the thread classes. For example, during theexecution of one or more multi-threaded processes within a virtualmachine, the control system may periodically take a thread dump of thevirtual machine. The thread dump may result in a stack trace for eachthread that is executing in the virtual machine. For each stack tracethat is received, the control system may analyze text contained in thestack trace to classify the associated thread and to update intensitystatistics tracked for all thread classes based on the stack trace.

In addition to classifying threads, embodiments may classify new stacksegments whenever they emerge at branch points along previouslyclassified stack segments. When the control system observes the firststack trace before any thread classes have been discovered, the controlsystem may consider the entire sequence of stack frames within the stacktrace to be linearly connected because the entire sequence of stackframes have only appeared together so far. In response, the controlsystem may initialize a thread class to classify the entire stack trace(i.e., the entire sequence of stack frames). As the control systemobserves subsequent stack traces that include varying sequences of stackframes, the control system can initialize additional thread classes toclassify each unique permutation of stack frames. In some cases, thecontrol system may observe a stack trace that does not share any stackframes (i.e., have any stack frames in common) with previously observedstack traces. In response, the control system may initialize a separatethread class to classify the new stack trace in its entirety.

More commonly however, the control system can observe a stack trace thatshares one or more stack frames with previously observed stack traces.Returning to FIG. 1 for example, suppose the first stack trace observedby the control system is {(A, B, D)} (i.e., the stack trace in sample 1or sample 2) where the stack trace contains the stack frames included instack segments A, B, and D. The control system may initialize a threadclass {(A, B, D)} to classify all threads that are observed to containthe stack frames included in stack segments A, B, and D. Next, supposethe second stack trace observed by the control system is {(A, C)} (i.e.,the stack trace in sample 6 or sample 7). In this regard, the controlsystem may determine that while the first and second stack traces aredifferent, the first and second stack traces share all of the stackframes included in stack segment A, which results in a branch point atstack segment A. In response, the control system may initialize a threadclass {(A, C}) to classify all threads that contain stack segments A andC on their call stacks.

It should be noted that because the stack frames in stack segment A hasbeen observed separately from the stack frames in stack segment (B, D),the stack segments A and (B, D) are no longer considered by the controlsystem to be linearly connected. Yet, the control system still considersthe stack frames in stack segment A to be linearly connected and thestack frames in stack segment (B, D) to be linearly connected. In thisregard, the control system may initialize several thread segmentcomponents of thread class {(A, B, D)} and thread class {(A, C)} toclassify the new stack segments formed by the newly discovered branchpoint. In particular, the control system may initialize a thread segment(A), a thread segment (B, D), and a thread segment (C), where the threadsegments (A) and (B, D) are components of the thread class {(A, B, D})and the thread segments (A) and (C) are components of the thread class{(A, C)}.

Some embodiments may use classification signatures to represent stacktraces and stack segments. In particular, trace signatures can be usedto represent stack traces of a particular thread class and segmentsignatures can be used to represent stack segments of a particularthread segment. Each trace signature may correspond to a tuple oflabeled binary trees that is built up via a synthesis and analysisprocess. Meanwhile, each segment signature of a thread segment maycorrespond to a node in the tuple that corresponds to the thread classof which the thread segment is a component of Later on in the analysisprocess, the tuples may be used like a parse tree (e.g., as part of aproduction grammar) to recognize incoming stack traces.

Returning to the above example, subsequent to the observation of thefirst stack trace but prior to the observation of the second stacktrace, the thread class {(A, B, D}) may correspond to a tuple of asingle binary tree. Because the entire sequence of frames within thefirst stack trace is considered to be a single stack segment, the singlebinary tree may include a single root node that represents the stacksegment (A, B, D). Subsequent to the observation of the second stacktrace, tuple may still include just a single binary tree. However, thebinary tree may now include three separate nodes: a root node thatrepresents the stack segment (A, B, D), a first child node of the rootnode that represents the stack segment (A), and a second child node ofthe root node that represents the stack segment (B, D). The process ofsynthesizing trace signatures and segment signatures are discussed infurther detail below with reference to FIGS. 4-6.

Each node in a binary tree may be uniquely identified by a label or anidentifier, which may be referred to as a compact code. In someembodiments, a thread of a particular thread class may be represented bythe one or more compact codes that identify each top-ranked node of thetuple that corresponds to the thread class. In a fashion similar toHuffman coding or other entropy coding schemes, some embodiments mayassociate shorter tuples to thread classes that are more popular (i.e.,have a higher thread intensity) and/or are discovered first. As aresult, more common types of threads can be compactly represented byshorter sequences of compact codes. In some embodiments, this may beensured by first analyzing the probability distribution of stack tracesin an offline analysis (i.e., offline processing) and feeding the stacktraces to the control system in descending order of frequency.

In embodiments that do not rely on offline analysis, the control systemmay receive stack traces in sequence with thread dumps that are takenperiodically from the one or more virtual machines (i.e., onlineprocessing).

The order in which different types of stack traces are observed may beaffected by the intensity of each type of stack trace. In other words,stack traces with higher intensities are statistically more likely to beobserved earlier in the sequence. Thus, such embodiments may assume that(1) the thread intensity of a particular thread class represents theassociated stack trace's probability of occurrence and (2) stack tracesassociated with higher intensity thread classes are often observedbefore stack traces associated with lower intensity thread classes. Inthis regard, the control system will naturally derive the most compactrepresentation for the highest intensity threads. Thus, by relying onthread intensity statistics rather than on offline processing, someembodiments can provide an optimal compression algorithm for stacktraces observed in response to a series of thread dumps.

A. Seasonality of Thread Intensity

Some embodiments can estimate, for each thread class that is identified,the seasonal trend for the thread class's intensity. As mentioned above,the intensity of a thread class or a thread segment may refer to astatistical measure of the “hotness” of the code blocks being referencedby the associated stack trace or stack segment. The hotness of a codeblock can be quantified by the number of invocations of the code blocktimes the execution time of the code block. A single raw threadintensity measure for a thread class may be the count of the number ofthreads of that thread class in a particular thread dump. An averagethread intensity measure per thread dump can correspond to the trafficintensity, offered load, or queue length of the thread type. Formean-ergodic processes, Little's formula can relate the expectedintensity {umlaut over (ρ)} (the expected number of arrivals during asampling interval corresponding to the expected response time{circumflex over (τ)}) to the expected response time {circumflex over(τ)} and the arrival rate λ, as shown below:{circumflex over (ρ)}=λ·{circumflex over (τ)}

In some embodiments, the seasonal trending process may use variablefilter parameters to account for irregular sampling intervals (e.g.,sampling heap usage and/or taking thread dumps) and to overcome theCauchy Distribution Problem. The process can also support sequentiallyfiltering multiple types of periods (e.g., weekday periods, weekendperiods, and holiday periods) with varying lengths (e.g., 1 day, 2days). Furthermore, the process can adjust, according to seasonality,the rate at which thread dumps are taken to reduce overhead whilemaintaining a particular confidence level for the thread intensitystatistics that are determined based on the thread dumps. In some cases,adjusting the thread dump rate may also minimize the volume of threaddump data that needs to be transported over a network (e.g., LAN, theInternet) to other machines (e.g., Big Data repository) for offlineprocessing.

In some embodiments, the seasonal trending process may partition weekdayperiods (i.e., 24 hour periods) into 96 fifteen minute intervals, whichresults in 96 seasonal indices (i.e., seasons) for each weekday period.The process may partition weekend periods (i.e., 48 hour periods) into192 fifteen minute intervals, which results in 192 seasonal indices foreach weekend period. Upon receiving a data set of a particular length(e.g., a time series recording thread dumps or heap usage over 10 days,which includes one or two weekends), the process can apply multi-periodtrending filters to weekday periods and weekend periods separately inorder to separate out seasonal patterns observed over single weekdaysand seasonal patterns observed over entire weekends, resulting in a setof 96 seasonal factors for the 96 seasonal indices of each weekday and aset of 192 seasonal factors for the 192 seasonal indices of eachweekend. The process may then renormalize the weekday seasonal factorsand the weekend seasonal factors so that a seasonal factor of ‘1’represents a common reference level for both weekday periods and weekendperiods.

It should be noted that if a seasonal factor larger than one is assignedto a seasonal index, that seasonal index has a higher than average valuein comparison to the rest of the period. On the other hand, if aseasonal factor smaller than one is assigned to a seasonal index, thatseasonal index has a lower than average value in comparison to the restof the period. For example, if the seasonal factor for the threadintensity of a particular thread class for the seasonal index thatcorresponds to the 9 AM-9:15 interval is 1.3, the average threadintensity of that particular thread class during the 9 AM-9:15 AMinterval is 30% higher than the average thread intensity of thatparticular thread class throughout an entire weekday.

In some embodiments, the seasonal trending process may separate outholidays (e.g., Labor Day, Christmas Day) as separate periods thatrepeat with a frequency of once every 12 months while weekday periodsrepeat every 24 hours and weekend periods repeat every 5 or 7 days. Theset of seasonal factors for such holiday periods may be renormalizedtogether with those of weekday periods and weekend periods so that theseasonal factor 1 represents a common reference level for all periods.Other frequencies for each period may be appropriate, as desired. Asexamples, holidays may be separated at a frequency of every 6 months orthe like while weekday may be periods repeat every 12 hours or the like.

In some embodiments, determining and tracking intensity statistics mayfurther include forecasting future values and the rate of change.However, the sampling interval can be irregular or even becomearbitrarily close to zero. In cases where the sampling interval becomesarbitrarily close to zero, the rate of change may become a randomvariable of the Cauchy Distribution, whose mean and standard deviationare undefined. To overcome the Cauchy Distribution problem with regardsto determining seasonal trends with adaptive sampling intervals, someembodiments may employ various adaptions of Holt's Double ExponentialFilter, Winter's Triple Exponential Filter, Wright's Extension forIrregular Time Intervals, Hanzak's Adjustment Factor for time-closeintervals, outlier detection, and clipping with adaptive scaling ofoutlier cutoff. The five sets of exponential filters can be sequentiallyapplied to the data set to estimate sets of seasonal factors for weekdayperiods and weekend periods.

B. Classification Signatures and Compression Scheme

Certain embodiments can assign a variable length sequence of compactcodes to the stack traces of threads where the length of sequencedepends on the intensity of the threads. An exemplary stack trace ispresented below:

oracle.jdbc.driver.T4CCallableStatement.executeForRows(T4CCallableStatement.java:991)oracle.jdbc.driver.OracleStatement.doExecuteWithTimeout(OracleStatement.java:1285)... oracle.mds.core.MetadataObject.getBaseMO(MetadataObject.java:1048)oracle.mds.core.MDSSession.getBaseMO(MDSSession.java:2769)oracle.mds.core.MDSSession.getMetadataObject(MDSSession.java:1188) ...oracle.adf.model.servlet.ADFBindingFilter.doFilter(ADFBindingFilter.java:150)...oracle.apps.setup.taskListManager.ui.customization.CustomizationFilter.doFilter(CustomizationFilter.java:46) ...weblogic.servlet.internal.WebAppServletContext.securedExecute(WebAppServletContext.java:2209)weblogic.servlet.internal.ServletRequestImpl.run(ServletRequestImpl.java:1457)... weblogic.work.ExecuteThread.execute(ExecuteThread.java:250)weblogic.work.ExecuteThread.run(ExecuteThread.java:213)

In the exemplary stack trace, the stack frame “oracle mds coreMetadataObject getBaseMO” below the Java Database Connectivity (JDBC)driver stack segment (i.e., the two stack frames each including“oracle.jdbc.driver . . . ”) indicates that the Meta Data Service (MDS)library invokes the JDBC operations that correspond to the JDBC stacksegment. The stack frame “oracle adf model servlet ADFBindingFilterdoFilter” below the MDS library stack segment (i.e., the three stackframes each including “oracle.mds . . . ”) indicates that the MDSoperations are invoked by an Application Development Framework (ADF)operation. As shown by the WebLogic stack segment (i.e., the four stackframes each including “weblogic . . . ”) at the bottom of the stacktrace, the ADF operation is invoked through a Hypertext TransferProtocol (HTTP) Servlet request.

As an example, a two-level Huffman coding scheme can be used to encodeand compress the above stack trace, resulting in a sequence of compactcodes that represents the exemplary stack trace. In the first level,compression tools (e.g., gzip) can detect substrings within the stacktrace such as “ServletRequestImpljava” and“weblogic.servlet.internal.ServletRequestImpl.run” and derive Huffmancodes for the substrings according to how frequently those substringsoccur in the stack trace. To increase the compression ratio, morefrequently occurring substrings may be assigned shorter Huffman codes.After the first level of compression, the compressed stack trace mayinclude, as metadata, an encoding dictionary that can be used to restorethe substrings from the Huffman codes.

The second level may involve applying another level of compression tothe compressed stack trace by replacing stack segments of the stacktrace with segment signatures. The steps of applying the second level ofcompression are discussed in further detail below with respect to FIGS.4-6.

C. Exemplary Data Structures

Classification signatures may be represented in memory via one or moreobject types. In particular, some embodiments may use aThreadClassificationInfo object to represent the classificationsignature of a thread class (i.e., a trace signature), a SegmentInfoobject to represent the classification signature of a thread segment(i.e., a segment signature), a StackFrameInfo object to represent eachelement in a linearly connected stack frames within stack segments, anda SeasonalTrendInfo object to encapsulate and track intensity statisticsfor a thread class or a thread segment.

Exemplary class/interface definitions that defineThreadClassificationInfo objects, SegmentInfo objects, StackFrameInfoobjects, and SeasonalTrendInfo objects are provided below:

public class ThreadClassificationInfo { long id; String name; shortnumOfOccur; short totalNumOfOccur; short numOfStackFrames; shortnumOfCoalescedSegments; List<SegmentInfo> segments; SeasonalTrendInfotrend; } public class SegmentInfo extends SegmentInfo { long id; Stringname; String dimension; short numOfOccur; short totalNumOfOccur;List<StackFrameInfo> elements; SegmentInfo firstSegment; SegmentInfosecondSegment; StackSegmentInfo coalescingSegment; Set<StackSegmentInfo>predecessors; Set<StackSegmentInfo> successors; SeasonalTrendInfo trend;Set<ThreadClassInfo> partOfThreadClasses; } public class StackFrameInfo{ long id; String name; short numOfOccur; short totalNumOfOccur;Set<StackFrameInfo> predecessors; Set<StackFrameInfo> successors;StackSegmentInfo coalescingSegment; String classMethodLineNumber; }public class SeasonalTrendInfo { List<long> posixTimestampOfMeasurement;List<short> rawMeasure; List<double> rawDeseasonalizedMeasure;List<double> smoothedMeasure; List<double>smoothedDeseasonalizedMeasure; double measureFilterConstant;List<double> measureWeightFactor; List<double> measureFilterParameter;List<double> rawGrowthRate; List<double> smoothedGrowthRate; doublerateFilterConstant; List<double> rateWeightFactor; List<double>rateFilterParameter; List<double> rawGrowthRateAcceleration;List<double> smoothedGrowthRateAcceleration; doubleaccelerationFilterConstant; List<double> accelerationWeightFactor;List<double> accelerationFilterParameter; List<double>rawWeekdaySeasonalFactor; List<double> rawWeekendSeasonalFactor;List<double> smoothedWeekdaySeasonalFactor; List<double>smoothedWeekendSeasonalFactor; double seasonalFactorFilterConstant;List<double> seasonalIndexWeightFactor; List<double>seasonalIndexFilterParameter; List<double> errorResidual; List<double>smoothedErrorResidual; List<double> smoothedAbsoluteErrorResidual;List<double> normalizedResidual; List<double> normalizedResidualCutoff;double errorResidualFilterConstant; List<double>errorResidualWeightFactor; List<double> errorResidualFilterParameter;List<double> localGrowthRateForecast; List<double>oneStepIntensityForecast; List<double> multiStepIntensityForecast; shortforecastHorizon; double[96] weekdaySeasonalFactor; double[192]weekendSeasonalFactor; }

As can be seen in the above definitions, each ThreadClassificationInfoobject, SegmentInfo object, and StackFrameInfo object includes a uniqueidentifier (i.e., id), a name, a counter that tracks the number of timesan object of the same type (e.g., same thread class, same threadsegment, same type of stack frame) was observed in the latest threaddump (i.e., numOfOccur), and another counter that tracks the number oftimes an object of the same type was observed in all thread dumps.

A ThreadClassificationInfo object can include a list of SegmentInfoobjects and a SeasonalTrendInfo object. In this regard, theThreadClassificationInfo may correspond to a tuple of binary trees whilethe list of SegmentInfo objects corresponds to the nodes making up thebinary trees. The SeasonalTrendInfo object may record intensitystatistics (e.g., a filter state) that pertain to the thread classrepresented by the ThreadClassificationInfo object.

A SegmentInfo object can include a list of StackFrameInfo objects, afirst child SegmentInfo object (i.e., firstSegment), a second childSegmentInfo object (i.e., secondSegment), a coalescing (i.e., parent)SegmentInfo object (i.e., coalescingSegment), a list of precedingsibling SegmentInfo objects (i.e., predecessors), a list of succeedingsibling SegmentInfo objects (i.e., successors), and a SeasonalTrendInfoobject. In this regard, the SegmentInfo object may correspond to a stacksegment. If the SegmentInfo object corresponds to a leaf node, the listof StackFrameInfo objects may correspond to the linearly connected stackframes included in the stack segment. If the SegmentInfo object bordersa branch point, the sibling SegmentInfo objects may correspond to stacksegments on the opposite side of the branch point while the coalescingSegmentInfo object may correspond to a parent stack segment thatincludes both the stack segment and a sibling stack segment. If theSegmentInfo object does not correspond to a leaf node, the childSegmentInfo objects may correspond to sub-segments of the stack segmentthat were created when a branch point was discovered in the stacksegment. The SeasonalTrendInfo object, may record intensity statisticspertaining to the thread segment represented by the SegmentInfo object.

Some embodiments may classify a stack segment of a stack trace byassociating a list of StackFrameInfo objects that are observed togetherwith a single SegmentInfo node. In other words, the SegmentInfo node isthe coalescing node of each of the StackFrameInfo objects of the stacksegment. Each StackFrameInfo object may have a single coalescingSegmentInfo node. When a branch point is detected somewhere along thelinearly connected StackFrameInfo objects of a SegmentInfo node, someembodiments may create two new SegmentInfo nodes and split the linearlyconnected StackFrameInfo objects into two sets of linearly connectedStackFrameInfo objects among the new SegmentInfo nodes. It can thenreconnect the two StackFrameInfo objects through a branch point.

Each of the new SegmentInfo nodes become the coalescing node of theStackFrameInfo objects in its part of the segment. Certain embodimentscan update the coalescingSegment of the StackFrameInfo objectscorrespondingly so that each StackFrameInfo object refers to the correctcoalescing SegmentInfo node. The two new SegmentInfo nodes arerepresented as a left sibling node and a right sibling node. The two newSegmentInfo nodes also become children of the original SegmentInfo node,which in turn becomes their parent. The parent SegmentInfo node canbecome the coalescing node of the two new SegmentInfo nodes.

The process of splitting stack segments in response to discovered branchpoints can result in a binary tree structure composed of SegmentInfonodes. This splitting process can be seen as bifurcation of a threadclass (i.e., a class of stack traces) into thread sub-classes. Someembodiments can continually split the stack segments into smaller stacksegments as the intensities of the individual stack frames in the stacksegments diverge over time, thereby enabling one to drill-down a threadclass hierarchy to observe how the intensity of a thread class can beproportionally attributed to the intensities of thread sub-classes.

In some embodiments, the SegmentInfo nodes in the interior of the binarytree are parent nodes whose StackFrameInfo objects are not all linearlyconnected because some stack frames are connected through branch points.In contrast, the StackFrameInfo objects of the leaf SegmentInfo nodescan be linearly connected. Within a SegmentInfo node, the linearlyconnected or branch-point connected StackFrameInfo objects can beoriented as a stack with a bottom StackFrameInfo and a topStackFrameInfo. By convention, the top StackFrameInfo object in the leftsibling SegmentInfo node can be connected to the bottom StackFrameInfoobject of the right sibling SegmentInfo node through a branch point.

Each SegmentInfo node may include a SeasonalTrendInfo object to trackthe intensity statistics of the thread (sub-)class represented by theSegmentInfo node. When splitting a SegmentInfo node into two newchildren SegmentInfo nodes, some embodiments can clone theSeasonalTrendInfo object of the SegmentInfo node into two newSeasonalTrendInfo objects and set one SeasonalTrendInfo object in eachof the children SegmentInfo nodes.

Some embodiments provide the ability to replicate the filter state of aparent SegmentInfo node to new child SegmentInfo nodes through thesplitting process. In doing so, some embodiments can continuously trackthe ratio of the intensity statistics among the parent and siblingSegmentInfo nodes. In particular, the intensity statistics of thechildren SegmentInfo nodes are each initially the same as that of theparent SegmentInfo node. However, as new samples are obtained, theintensity statistics of the children SegmentInfo nodes may begin todiverge from that of the parent and from each other. The filter statesof the new stack segments begin to deviate from each other and thefilter state of the original stack segment as the filter states of thenew stack segments are separately updated.

In some cases, intensity statistics among parent and sibling SegmentInfonodes can converge to a ratio over time. Some embodiments can apply theparent-child and sibling relationships among the SegmentInfo nodes todefine correlation models for multivariate state estimation techniques.In particular, if the process is stationary, the ratio of the intensitystatistics among the related SegmentInfo nodes may converge to astationary state. In particular, if a process is strict-sense orwide-sense stationary, the first and second moments of the jointprobability distributions of intensity statistics among relatedSegmentInfo nodes, which may include the mean, variance,auto-covariance, and cross-covariance of the related SegmentInfo nodesmay not vary with respect to time. Thus, the ratio of intensitystatistics among the parent and sibling SegmentInfo nodes can beexpected to converge over time. Thus, by continuously tracking theintensity statistics of the sibling SegmentInfo nodes through branchpoints and determining that the ratio of intensity statistics among theparent and sibling SegmentInfo nodes converge over time, someembodiments can use the ratios to define correlation models formultivariate state estimation techniques. The resulting models can beused for anomaly detection and generating predictions.

A StackFrameInfo object can include a one or more precedingStackFrameInfo objects and/or one or more succeeding StackFrameInfoobjects (i.e., predecessors and successors), a coalescing SegmentInfoobject (i.e., coalescingSegment), and information that identifies codereferenced by the StackFrameInfo object (i.e., classMethodLineNumber).If the StackFrameInfo object is not adjacent to a branch point, theStackFrameInfo object can be linearly connected to a single predecessorstack frame and a single successor stack frame. The StackFrameInfoobject can refer to the containing SegmentInfo object by the membervariable coalescingSegment.

When it comes time to process the latest thread dump, the membervariable numOfOccur for every ThreadClassificationInfo object,SegmentInfo object, and StackFrameInfo object can be reset to 0. Eachstack trace obtained from the thread dump may be parsed from the bottomto the top of the stack trace. After applying the first level of theHuffman coding scheme to compress the stack trace, each line of thestack trace may be parsed into a StackFrameInfo object. After parsingthe list of StackFrameInfo objects into a list of SegmentInfo objects,some embodiments may attempt to match the list of SegmentInfo objects toa ThreadClassificationInfo object that contains a matching list ofSegmentInfo objects. If such a ThreadClassificationInfo object does notexist, some embodiments may register a new ThreadClassificationInfoobject to represent the list of SegmentInfo objects. Afterwards, someembodiments may then update the numOfOccur and totalNumOfOccur membervariables of the matching/new ThreadClassificationInfo object and eachSegmentInfo object and StackFrameInfo object in the matching/newThreadClassificationInfo object. Note that if a SegmentInfo node is aleaf level node, the numOfOccur member variable of the node will beequivalent to that of each StackFrameInfo element in the SegmentInfonode.

Next, some embodiments can update intensity statistical measuresencapsulated in associated SeasonalTrendInfo objects. In particular,some embodiments may update the rawMeasure member variables in eachSeasonalTrendInfo object by setting the rawMeasure to the numOfOccurmember variable of the containing ThreadClassificationInfo object orSegmentInfo object. Note that in some embodiments, the rawMeasure mayonly be updated every N thread dumps, in which case the rawMeasure of aSeasonalTrendInfo object is set to the corresponding numOfOccur dividedby N. In some embodiments, such embodiments may update the rawMeasuremember variable of a SeasonalTrendInfo object only when the numOfOccurmember variable of the associated ThreadClassificationInfo object or theassociated SegmentInfo object is not zero. If the numOfOccur membervariable is not zero, then the rawMeasure of the SeasonalTrendInfoobject is set to the value of numOfOccur divided by N, where N is thenumber of thread dumps since the last update of rawMeasure. In suchembodiments, the method treats the case of when the numOfOccur is zeroas if no measurement is available. In this regard, when no measurementis available, the rawMeasure is not updated. Stated another way, suchembodiments track the number of thread dumps since the last update ofthe rawMeasure ‘N’. The thread intensity measurements may correspond toan irregular time series. It should be noted that exponential filtersfor irregular time intervals (e.g., Holt's Double Exponential andWinter's Triple Exponential Filter, disclosed above) can effectivelyfilter the rawMeasure to get a de-seasonalized measure and a seasonalfactor from a set of measurements taken at irregular time intervals.

It should be noted that each SeasonalTrendInfo object can includetime-series data generated by five sets of exponential filters beingapplied to each of the following statistical measurements: the rawmeasure of thread intensity, the rate at which the thread intensity isincreasing or decreasing, the acceleration or deceleration of the rate,the seasonal factor for the thread intensity, and the residualcomponent. Within a SeasonalTrendInfo object, the states of the fivesets of exponential filters for the variables, the filter constants,filter parameter adjustment weight factors (to adjust for irregular timeintervals between samples), and filter parameters can be represented bythe time-series data.

D. Exemplary Generation of Classification Signatures

FIG. 3 depicts exemplary thread dumps of a virtual machine 300 over aperiod of time, according to some embodiments. In contrast with the 100ms to one second sampling interval runtime profiling in FIG. 1, thesampling interval employed by the control system in FIG. 3 may be longer(e.g., between 20 seconds and one minute) to reduce sampling overhead.As shown in FIG. 3, within two to three sampling intervals, processesexecuting within the virtual machine 300 spawn the threads 302, 304,306, 308, 310, and 312. Each of the threads 302-312 are associated witha separate call stack while executing and can thus produce a stack tracewhen a thread dump is taken. FIG. 3 depicts a total of three threaddumps being taken: thread dump N, thread dump N+1, and thread dump N+2.

FIG. 3 shows three different types of stack traces being observed in theorder (A,B,D), (A,B,D), (A,C), and (A,B,E) in three consecutive threaddumps. The stack trace (A,B,D) is observed twice. Before thread dump Nis taken, the thread 302 is spawned and begins executing. When threaddump N is taken, a stack trace (A,B,D) observed for the thread 302. Itshould be noted that even though stack segment A, stack segment B, andstack segment D have yet to be identified, for ease of explanation, thenames of the stack segments will be used throughout the example depictedin FIG. 3. As a sampling interval elapses after thread dump N is taken,the thread 302 finishes, the thread 304 is spawned and finishes withoutever being sampled while the threads 306 and 308 are spawned. Whenthread dump N+1 is taken, the thread 308 yields a stack trace (A,B,D)while the thread 310 yields stack trace (A,C). As another samplinginterval elapses after thread dump N+1 is taken, the threads 306 and 308finish, the thread 310 is spawned and finishes without ever beingsampled, and the thread 312 is spawned. When thread dump N+2 is taken,thread 312 yields stack trace (A,B,E). As can be seen in FIG. 3, the(A,B,D) thread type is the first type of thread to be observed and the(A,B,D) thread type has a higher intensity than the (A,C) or (A,B,E)thread types.

After thread dump N, the control system can register the singleSegmentInfo(A,B,D) node as the classification signature for the stacktrace (A,B,D). The control system may then associate aSeasonalTrendInfo(A,B,D) object with the SegmentInfo(A,B,D) node andupdate the state encapsulated by the node:

SegmentInfo(A,B,D).numOfOccur = 1. SegmentInfo(A,B,D).totalNumOfOccur =1.

FIG. 4 depicts a set of classification signatures 400 including a singleclassification signature 450 that has been registered in response to thestack trace (A,B,D). As can be seen in FIG. 4, the classificationsignature 450 includes a single node 402 that corresponds toSegmentInfo(A,B,D), where SegmentInfo(A,B,D) is shown to be thecoalescing node of all stack frames a1-d3 of the stack trace.

When stack trace (A,B,D) is observed again in thread dump N+1, thecontrol system may update the SegmentInfo(A,B,D) node as follows:

SegmentInfo(A,B,D).numOfOccur = 1. SegmentInfo(A,B,D).totalNumOfOccur =2.

When stack trace (A,C) is observed for the first time in thread dumpN+1, the control system determines that the entire set of stack frameswithin the stack segment (A,B,D) are no longer linearly connected. Abranch point now exists between the last stack frame (e.g., going fromtop to bottom of the stack trace) of the set of stack frames representedby ‘A’ and the first stack frame of the set of stack frames representedby ‘B,D’ because, in any given stack trace, the next stack frame thatfollows the last stack frame could be (1) the first stack frame of (B,D)or (2) the first stack frame of the set of stack frames represented by‘C’. Thus, the control system may split the stack segment (A,B,D) intostack segment (A) and stack segment (B,D) by creating the nodesSegmentInfo(A) and SegmentInfo(B,D) and assigning the two nodes to bechildren of SegmentInfo(A,B,D). For stack trace (A,C), the controlsystem may initialize stack segment (C) by creating the nodeSegmentInfo(C) and register an ordered tuple including SegmentInfo(A)and SegmentInfo(C) as the classification signature for the stack trace(A,C).

In some embodiments, the control system may clone theSeasonalTrendInfo(A,B,D) object into SeasonalTrendInfo(A) andSeasonalTrendInfo(B,D) objects for the nodes SegmentInfo(A) andSegmentInfo(B,D), respectively, and create a new SeasonalTrendInfo(C)for SegmentInfo(C) as follows:

SeasonalTrendInfo(A) ← SeasonalTrendInfo(A,B,D) SeasonalTrendInfo(B,D) ←SeasonalTrendInfo(A,B,D) SeasonalTrendInfo(C) ← new SeasonalTrendInfo

The control system may also update the above SegmentInfo nodes asfollows:

SegmentInfo(A).numOfOccur = 2 SegmentInfo(A).totalNumOfOccur = 3SegmentInfo(C).numOfOccur = 1 SegmentInfo(C).totalNumOfOccur = 1

FIG. 5 depicts a set of classification signatures 500 including theclassification signature 450 and a new classification signature 550 thatwas generated in response to observing stack trace (A,C) for the firsttime. As can be seen in FIG. 5, the classification signature 450 nowincludes three nodes: node 402, nodes 502, and node 504. Node 402corresponds to SegmentInfo(A,B,D), which is the coalescing node of node502 and node 504. Node 502 corresponds to SegmentInfo(A), whichcoalesces stack frames a1-a3. Node 504 corresponds to SegmentInfo(B,D),which coalesces stack frames b1-d3. The classification signature 550includes two nodes: node 506, which corresponds to SegmentInfo(A) shownto coalesce stack frames a1-a3, and node 508, which corresponds toSegmentInfo(C) shown to coalesce stack frames c1-c3.

When stack trace (A,B,E) is observed for the first time in thread dumpN+2, the control system determines that the entire set of stack frameswithin the stack segment (B,D) are no longer linearly connected. Abranch point now exists between the last stack frame of the set of stackframes represented by ‘B’ and the first stack frame of the set of stackframes represented by ‘D’ because, in any given stack trace, the nextstack frame that follows the last stack frame could be (1) the firststack frame of (D) or (2) the first stack frame of the set of stackframes represented by ‘E’. Thus, the control system may split the stacksegment (B,D) into stack segment (B) and stack segment (D) by creatingthe nodes SegmentInfo(B) and SegmentInfo(D) and assigning the two nodesto be children of SegmentInfo(B,D). For stack trace (A,B,E), the controlsystem may initialize stack segment ‘E’ by creating the nodeSegmentInfo(E) and register an ordered tuple including SegmentInfo(A),SegmentInfo(B), and SegmentInfo(E) as the classification signature forthe stack trace (A,B,E).

In some embodiments, the control system can clone theSeasonalTrendInfo(B,D) object into SeasonalTrendInfo(B) andSeasonalTrendInfo(D) objects for the nodes SegmentInfo(B) andSegmentInfo(D), respectively, and create a new SeasonalTrendInfo(E) forSegmentInfo(E) as follows:

SeasonalTrendInfo(B) ← SeasonalTrendInfo(B,D) SeasonalTrendInfo(D) ←SeasonalTrendInfo(B,D) SeasonalTrendInfo(E) ← new SeasonalTrendInfo

The control system may also update the above SegmentInfo nodes asfollows:

SegmentInfo(A).numOfOccur = 1 SegmentInfo(A).totalNumOfOccur = 4SegmentInfo(B).numOfOccur = 1 SegmentInfo(B).totalNumOfOccur = 3Segmentlnfo(E).numOfOccur = 1 Segmentlnfo(E).totalNumOfOccur = 1

FIG. 6 depicts a set of classification signatures 600 including theclassification signatures 450 and 550 and a new classification signature650 that was generated in response to the stack trace (A,B,E). As can beseen in FIG. 6, the classification signature 450 now includes fivenodes: node 402, node 502, node 504, node 602, and node 604. Node 504corresponds to SegmentInfo(B,D), which is the coalescing node for node602 and node 604. Node 602 corresponds to SegmentInfo(B), whichcoalesces stack frames b1-b3. Node 604 corresponds to SegmentInfo(D),which is the coalescing node for stack frames d1-d3. The classificationsignature 550 has not changed. The classification signature 650 includesthree nodes: node 606, which corresponds to SegmentInfo(A) shown tocoalesce stack frames a1-a3, node 608, which corresponds toSegmentInfo(B) shown to coalesce stack frames b1-b3, and node 610, whichcorresponds to SegmentInfo(E) shown to coalesce stack frames e1-e3.

As shown in FIG. 6, the classification signature for the stack trace(A,B,D) can be comprised of a single SegmentInfo node at the root of theclassification signature 450. In other words, stack trace (A,B,D), whichis the highest intensity stack trace, has the most compactrepresentation. Meanwhile, stack trace (A,C) is assigned the secondshortest classification signature with the two ordered nodes (A) and(C). Stack trace (A,B,E), which was detected last, is assigned the thirdshortest classification signature with the three ordered nodes (A), (B),and (E). As shown in FIGS. 4-6, a ThreadClassificationInfo object maycorrespond to a tuple of SegmentInfo nodes and a SegmentInfo node mayrefer to binary trees (or sub-trees that are binary) of otherSegmentInfo nodes and/or sets of StackFrameInfo objects. Together, theThreadClassificationInfo objects, SegmentInfo nodes, and theStackFrameInfo objects may constitute the production grammar:

Thread1 −> (A,B,D) Thread2 −> (A)(C) Thread3 −> (A)(B)(E) (A,B,D) −>(A)(B,D) (B,D) −> (B)(D) A −> a1,a2,a3 B −> b1,b2,b3 C −> c1,c2,c3 D −>d1,d2,d3 E −> e1,e2,e3

As can be seen above, the individual stack frames ai, bi, ci, di, ei areterminals while the SegmentInfo nodes are non-terminals of the grammar.Some embodiments can parse the stack frames of a stack trace from thebottom of the stack trace to the top of the stack trace (oriented asleft to right in the following notation).

a1,a2,a3,b1,b2,b3,d1,d2,d3 (A),b1,b2,b3,d1,d2,d3 use production (A) −>a1,a2,a3 (A),(B),d1,d2,d3 use production (B) −> b1,b2,b3 (A),(B),(D) useproduction (D) −> d1,d2,d3 (A),(B,D) use production (B,D) −> (B)(D)(A,B,D) use production (A,B,D) −> (A),(B,D) Thread1 use productionThread1 −> (A,B,D)

As can be seen above, some embodiments can analyze the stack frames viabottom-up syntax analysis, which may be similar to shift-reduce parsingor left to right “LR” parsing. The analysis can involve shifting andreducing the stack frames and SegmentInfo nodes to construct a parsetree for the stack trace by working from the leaves to the root of thetree. Some embodiments can synthesize the parse tree for an earlieroccurrence of the stack traces of a thread and analyze the stack tracesof another occurrence of the thread by reducing (i.e., shift-reduceparsing, left to right “LR” parsing) to the same parse tree. Each nodeof the classification tree can be a compact label for a class of stacktraces and the root of the classification tree can be a compact labelfor a class of threads.

FIG. 7 illustrates a flowchart 700 of a process for generating and/ormodifying one or more thread classification signatures in response to athread dump according to some embodiments. In some embodiments, theprocess depicted in flowchart 700 may be implemented by a computersystem with one or more processors (e.g., computer system 1700 of FIG.17) where the one or more processors can execute the steps based oncomputer code stored in a computer-readable medium. The steps describedin FIG. 7 can be performed in any order and with or without any of theother steps.

Flowchart 700 begins at step 702, where embodiments perform a threaddump during an execution of a multi-threaded program. In particular,some embodiments may correspond to one or more monitoring processes thatmonitor a software execution environment in which the multi-threadedprogram executes. The software execution environment may support aplurality of multi-threaded processes that include the multi-threadedprogram. In some cases, the software execution environment may be avirtual machine that supports the taking of thread dumps. In someembodiments, one or more monitoring processes may execute within thevirtual machine alongside the multi-threaded program. In someembodiments, the one or more monitoring processes may execute separatelyfrom the virtual machine on the same set of machines or on a differentset of machines. The one or more monitoring processes may periodicallyinitiate a thread dump of the virtual machine. For a particular threaddump, stack traces may be obtained for each thread that is executing onbehalf of the (e.g., spawned by) the multi-threaded program at the timethe particular thread dump is taken.

At step 704, embodiments receive a stack trace for each thread that wasexecuting during the thread dump. The stack trace for a particularthread may correspond to one or more lines of text that describe thethread's call stack. Each line within the stack trace corresponds to aparticular stack frame on the thread's call stack and may describe thecode block associated with the stack frame. In some embodiments, thestack frame may include a source code file and line number that pointsto the code block and a class name and/or method name associated withthe code block.

At decision 706, embodiments determine whether another stack trace needsto be analyzed. If not, the flowchart ends at step 716. In particular,once all of the stack traces of a thread dump have been analyzed by theone or more monitoring processes, some embodiments may update intensitystatistics encapsulated by one or more objects in memory. For example,member variables of one or more SeasonalTrendInfo objects (e.g.,rawMeasure, rawDeseasonalizedMeasure, smoothedWeekdaySeasonalFactor,and/or smoothedWeekendSeasonalFactor) may be updated based on what sortof stack traces are obtained from the thread dump.

Otherwise, at step 708, embodiments determine whether an existing tracesignature represents the sequence of stack frames included by the stacktrace. In particular, some embodiments may use, as a production grammar,an existing set of classification signatures that have been built upbased on the stack frames received from previous thread dumps todetermine whether the sequence of stack frames can be represented by oneof the existing signatures. This may involve one or more shift-reduceoperations where portions of the stack trace are collapsed into leafSegmentInfo nodes and the SegmentInfo nodes themselves are collapsedinto coalescing nodes. If the shift-reduce operations results in anordered-tuple that is registered as a classification signature, thatclassification signature represents the sequence of stack framesincluded by the stack trace.

At decision 710, if such a trace (i.e., classification) signatureexists, the flowchart proceeds to step 714. Otherwise, at step 712,embodiments generate a new trace signature that represents the sequenceof stack frames included by the stack trace. In other words, a branchpoint within a set of stack frames that were thought to be linearlyconnected has been discovered. Some embodiments may then generate one ormore SegmentInfo nodes, modify one or more binary trees, and/or modifyone or more ordered tuples to generate a new classification signaturethat represents the set of (formerly) linearly connected stack framesincluded by the stack trace. The technique of generating the newclassification signature is described in further detail below withrespect to FIG. 8.

At step 714, embodiments increment a counter associated with the tracesignature before returning to decision 706. In particular certaincounters that are members of ThreadClassificationInfo objects,SegmentInfo objects, and/or StackFrameInfo objects (e.g., numOfOccurand/or totalNumOfOccur) may be incremented to track the number of stacktraces, stack segments, and stack frames by type as they are receivedand discovered.

FIG. 8 illustrates a flowchart 800 of a process for generating ormodifying a thread classification signature in response to detecting abranch point according to some embodiments. In some embodiments, theprocess depicted in flowchart 800 may be implemented by a computersystem with one or more processors (e.g., computer system 1700 of FIG.17) where the one or more processors can execute the steps based oncomputer code stored in a computer-readable medium. The steps describedin FIG. 8 can be performed in any order and with or without any of theother steps.

Flowchart 800 begins at step 802, where embodiments determine whetherone or more SegmentInfo nodes have been previously generated. If so, theflow chart proceeds to step 804. Otherwise, the flowchart proceeds tostep 814. Unless the stack trace currently being analyzed is the firststack trace received for the data set, the set of classificationsignatures will likely contain one or more classification signaturespreviously generated for prior stack traces, where the classificationsignatures include SegmentInfo nodes. Because types of stack tracesreceived from the same process are likely to share stack segments witheach other, any type of stack trace received for the first time willlikely result in the discovery of branch points.

At step 804, embodiments determine one or more subsequences of stackframes included in the sequence of stack frames included by the stacktrace that are not represented by any previously generated node. Inparticular, some embodiments may consult existing classificationsignatures and SegmentInfo nodes while attempting to compress thesequence of stack frames contained by the stack trace through a seriesof shift-reduce operations. Any subsequences of stack frames of thesequence that cannot be reduced may be determined to be a new type ofstack segment. In this case, some embodiments may determine that aSegmentInfo node that represents the new type of stack segment needs tobe generated.

At step 806, embodiments generate one or more additional nodes torepresent the one or more subsequences of stack frames. In particular, anew StackFrameInfo object may be generated for each stack frame includedin the new type of stack segment. A new SegmentInfo node thatcorresponds to the new type of stack segment may be generated, where thenew SegmentInfo node refers to each of the new StackFrameInfo objects.

At step 808, embodiments incorporate at least one of the one or moreadditional nodes into one or more previously generated binary trees ofone or more previously generated tuples. One or more binary trees of oneor more existing classification signatures may be modified and/orexpanded to account for the newly discovered branch point. In caseswhere a stack segment represented by a leaf SegmentInfo node of anexisting binary tree is split by the new branch point, that leaf nodemay become the coalescing node of two new leaf SegmentInfo nodes.

At step 810, embodiments generate one or more additional binary trees,wherein at least one or more the one or more binary trees include atleast one of the one or more additional nodes. In many cases, the one ormore additional binary trees may be single level trees having a singlenode. One of the newly generated binary trees may include the newSegmentInfo node generated in step 806.

At step 812, embodiments generate an additional tuple that includes theone or more additional binary trees to represent the stack trace. Theadditional tuple may correspond to the classification signature thatrepresents the newly discovered type of stack trace. Some tuples may beordered sets of single-level binary trees that each contain a singlenode and may look similar to a list of nodes. Other tuples maycorrespond to a single multi-level binary tree. Still yet other tuplesmay include single-level binary trees and multi-level binary trees incombination. In general, as more and more types of stack traces arediscovered, each subsequent classification signature that is generatedmay correspond to longer and longer ordered tuples. However, becausecommon types of stack traces are more likely to be encountered first,the longer classification signatures are more likely to represent stacktraces that occur less often. This may ensure that a higher percentageof stack traces are compressed into shorter classification signatures.After step 812, the flowchart ends at step 820.

At step 814, embodiments generate a tuple that includes a single binarytree that includes a single node to represent the stack trace. Becauseno SegmentInfo nodes have been found, the currently analyzed stack traceis likely to be the first. As a result, some embodiments may generate aclassification signature that corresponds to a single binary tree withonly one SegmentInfo node. After step 814, the flowchart ends at step820. As different types of stack traces as encountered in the future,the binary tree may be expanded with new SegmentInfo nodes to representnewly encountered branch points.

IV. Heap Usage Measurements at Irregular Time Intervals

Some embodiments may have the control system monitor the time seriesdata for heap allocation (i.e., heap usage) to estimate trends and toforecast future memory usage within a virtual machine. By detectingseasonal trends and forecasting the memory capacity requirements, someembodiments can dynamically reallocate shared system memory amongvirtual machines, thereby enabling elasticity in resource allocation.Forecasting of capacity requirements may involve the estimation of theheap's growth rate. To ensure sample accuracy, heap allocationmeasurements may be taken during full garbage collection (GC) cycles,which occur at irregular time intervals. Estimation of heap growth ratemay involve division by random time intervals which is complicated bythe irregular time intervals that intermittently get arbitrarily closeto zero. The noise in growth rate measurement is a ratio of two Gaussiandistributions yielding a Cauchy distribution, which can be hard tofilter. The mean and standard deviation of the Cauchy distribution areundefined in the sense that a large number of data points do not yieldmore accurate estimate of the mean and standard deviation than does asingle data point. Increasing the pool of samples can increase thelikelihood of encountering sample points with a large absolute valuecorresponding to division by a time close interval.

It should be noted that, unlike heap size measurements whose samplingintervals are irregular due to the irregularity of full GC cycles, thethread intensity measurements can be sampled at regular intervals toavoid time-close intervals. Even so, the same techniques describedherein for trending of heap allocation can be applied to seasonaltrending and forecasting of thread and stack segment intensitymeasurements. In some embodiments, the techniques can adjust forvariable latencies due to the CPU scheduling of the threads and theinteference of the full GC cycles. The techniques can also adjust forthe variable sampling intervals due to the variable computation timerequired to classify the stack segments. In situations where aparticular thread or stack segment has not been observed in a threaddump, some embodiments may leave the numOfOccur member variable of theassociated ThreadClassificationInfo object or the associated SegmentInfoobject as zero, which may indicate that no measurement for theparticular thread or stack segment is available. Such embodiments maynot update the rawMeasure variable of a SeasonalTrendInfo object. Suchembodiments may update the rawMeasure member variable of aSeasonalTrendInfo object only when the numOfOccur member variable of theassociated ThreadClassificationInfo object or the associated SegmentInfoobject is not zero. Such embodiments may track the number of threaddumps ‘N’ since the last update of the rawMeasure. The thread intensitymeasurements may correspond to a series with irregular time intervals.

A Holt-Winter triple exponential filter, published in 1957 and 1960, canbe used for seasonal trending and forecasting. C. C. Holt, “ForecastingTrends and Seasonal by Exponentially Weighted Averages,” Office of NavalResearch Memorandum, no. 52 (1957) is incorporated by reference herein.P. R. Winters, “Forecasting Sales by Exponentially Weighted MovingAverages,” Management Science, vol. 6, no. 3, p. 324-342 (1960) isincorporated by reference herein. Wright extended the Holt-Winterformulae in 1986 to support irregular time intervals. D. J. Wright,“Forecasting data published at irregular time intervals using anextension of Holt's method,” Management Science, vol. 32, no. 4, pp.499-510 (1986) is incorporated by reference herein. In 2008, Hanzakproposed an adjustment factor for time-close intervals. T. Hanzak,“Improved Holt Method for Irregular Time Series,” WDS'08 ProceedingsPart I, pp. 62-67 (2008) is incorporated by reference herein.

The adjustment factor for time close intervals, which is meant tocompensate for higher relative intensity of noise due to a randomtime-close interval in the rate estimate, can inadvertently dampen therate of change estimates if the time interval decreases monotonicallyduring a congestion caused by memory leaks or deadlocks. Non-linear orpolynomial time complexity of full GC algorithms can result indecreasing thread runtime intervals as congestion worsens. In case ofmemory leaks, as the time interval decreases, the run time can decreasebut the measurement time can increase because the virtual machine can befrozen longer due to full GCs being performed more often. If the virtualmachine is frozen during a full GC, new requests can be queued upoutside the virtual machine. The backlog can accelerate the rate ofchange of the heap usage during the subsequent run time. In someembodiments, Hanzak's adjustment for time-close intervals is used fortrending and forecasting of heap allocation and to track theaccelerating heap growth rate.

In an embodiment of the invention, Holt-Winter triple exponential filtercan be applied for seasonal trending and forecasting of heap usage toefficiently achieve elasticity in memory allocation. The standardHolt-Winter triple exponential filter, which can be applied to demandforecasting from regular time series, can be specially adjusted to workfor the random time intervals with irregular time-close intervals.Embodiments of the invention can apply the Wright formula for irregulartime intervals and Hanzak's adjustment for time-close intervals fortrending and forecasting of heap allocation. A non-trivial selection ofa structure of the filters suitable for the irregular time intervalsresulting from full GCs can be performed. The structure of theHolt-Winter-Wright-Hanzak filters can be derived from first principlesto systematically devise the adaptations to match the time seriesgenerated by full GC cycles.

In some embodiments, formulae for exponential moving averages areapplied to smooth out time-series data, locally linear trend, seasonaltrend, error residual of forecast, and absolute deviation of forecastfor monitoring and forecasting of resource utilization measures such asheap memory usage and thread intensity. In some embodiments, theformulae can be based on Brown's exponential filter proposed in 1956,Holt's double exponential filter proposed in 1957, Winters' tripleexponential filter proposed in 1960, Wright's extension for irregulartime intervals proposed in 1986, Hanzak's adjustment factor fortime-close intervals proposed in 2008, and outlier detection andclipping. The following publications are included by reference herein:R. G. Brown, “Exponential Smoothing for Predicting Demand,” Cambridge,Arthur D. Little Inc. (1956), p. 15; C. C. Holt, “Forecasting Trends andSeasonal by Exponentially Weighted Averages,” Office of Naval ResearchMemorandum, no. 52, (1957); P. R. Winters, “Forecasting Sales byExponentially Weighted Moving Averages,” Management Science, vol. 6, no.3, p. 324-342, (1960); D. J. Wright, “Forecasting data published atirregular time intervals using an extension of Holt's method,”Management Science, vol. 32, no. 4, pp. 499-510 (1986); T. Hanzak,“Improved Holt Method for Irregular Time Series,” WDS′08 ProceedingsPart I, pp. 62-67 (2008); and S. Maung, S. W. Butler and S. A. Henck,“Method and Apparatus for process Endpoint Prediction based on ActualThickness Measurements,” U.S. Pat. No. 5,503,707 (1996).

V. Correlating Thread Intensity and Heap Usage

Various embodiments provide techniques for identifying heap-hoardingstack traces (i.e., classes of threads) within multi-threadedapplications by correlating trends between intensity statistics ofvarious classes of threads spawned by the application and heap usagestatistics. In doing so, some embodiments may identify, based on heapusage statistics, seasons where high heap usage tends to be high (i.e.,high heap usage seasons) within a time period during which one or moremulti-threaded applications are executing within a software executionenvironment. As explained above, some embodiments may then identify andcollect intensity statistics for multiple classes of threads through theanalysis of thread dumps obtained from the software executionenvironment in the same time period of the high heap usage seasons. Someembodiments may then identify “heap-hoarding” classes of threads (i.e.,heap hoarding stack traces) from amongst the identified classes ofthreads by ranking the classes of threads by the degree of correlationbetween their intensity statistics and the high heap usage trends.

Some embodiments may refer to such classes of threads as heap-hoardingbecause there is a high probability that the code being executed by suchthreads is inefficient in terms of heap memory usage. Stated anotherway, erroneously written code and/or unoptimized code executed by thesethreads may cause the threads to hoard a large amount of heap memory,thereby contributing significantly to the high heap usage trend.

It should be noted that such memory hotspots are important from theperspective of operating cloud-based services over long periods of timein a production environment. Accordingly, by enabling the continuousdetection and mitigation of such hotspots, some embodiments may directlyimpact the operational efficiency of the cloud services. It should alsobe noted that such embodiments may be advantageous over using memoryprofiler tools to profile such applications because such tools may addtoo much overhead to the application. Accordingly, memory profiler toolsmay not be practical for continuously profiling an application that isexecuting in a production environment.

A. Inefficient Heap Usage in Code

One common cause of inefficient memory usage is due to local variablesdefined in the stack frames of a thread. In general, when a runningthread instantiates an object, that object occupies heap memory untilthe number of stack frames that refer (directly or indirectly) to theobject falls to zero, at which point the heap memory is freed at thenext garbage collection. Accordingly, local variables that referenceslarge objects from stack frames that remain active over a long period oftime may inadvertently contribute significantly to heap memory usagebecause they don't allow the objects to be garbage collected.

Some embodiments suppose that a fraction ‘p’ of the total heap usage ‘G’bytes can be attributed to a class of threads ‘C’. Further, someembodiments may also suppose that the average heap usage among thisclass of threads ‘C’ (i.e., heap usage per thread) is ‘M’ bytes. In thisinstance, let ‘T_(C)’ denote the expected number of threads of the classof threads ‘C’. The following relation gives ‘T_(C)’, which is definedas the thread intensity in the statistical model:

$T_{C} = \frac{pG}{M}$

In response to identifying heap-hoarding classes of threads, certainembodiments may report (e.g., via a notification or an alert) theclasses of threads to developers, performance engineers, and otherrelevant personnel. As a result, code associated with such types ofthreads may be subject to detailed code review and code profiling. Insome cases, certain associated stack frames may be inspected. Forexample, an investigation may involve taking a heap dump during the timewhen the heap usage is near a seasonal peak to inspect the stack framesincluded in the stack traces of heap-hoarding threads. The stack framescan contain the local variables referencing the objects contributing tothe high heap usage (e.g., objects occupying large amounts of heapmemory). This kind of code inspection and optimization can be done byvisual code review, automatic code review, profiling of the identifiedthreads, just-in-time compiler optimization, dynamic byte-codeinjection, or combinations of these techniques. In some embodiments,heap-hoarding classes of threads may be reported to other automatic codeoptimization tools to leverage their code optimization functionalities.

Some embodiments may automatically redesign or rewrite application codeto make its usage of memory more efficient. For example, someembodiments can automatically rewrite code so that local variablesrelease large objects as soon as possible without changing the behavioror correctness of the application. In some cases, this may involve deepanalysis of the code paths involved in the heap-hoarding threads.

For example, consider the following code:

fileOS.write(buffer.toString( ).getBytes( ));

Some embodiments may determine that the above code is inefficient withrespect to memory usage because three objects: buffer, buffer.toString() and buffer.toString( ).getBytes( ), are held by local variables in astack frame of a heap-hoarding thread. In particular, the localvariables prevent the three objects from being garbage collected whilethe thread is blocking in a file system call.

Some embodiments can modify the code as shown below so that at least twoobjects: buffer and buffer.toString( ), can be garbage collected whilethe thread is blocking in a file system call:

String temp1 = buffer.toString( ); buffer = new StringBuffer( ); //allow garbage collection of the old buffer byte[ ] temp2 =temp1.getBytes( ); temp1 = null; // allow garbage collection of thestring fileOS.write(temp2); // this is a blocking call temp2 = null; //allow garbage collection of the bytes array

Some embodiments can use non-intrusive ways to inspect the stack framesof the heap-hoarding stack traces.

B. Initializing Seasonal Factors for Weekday and Weekend Periods

To identify the heap-hoarding stack traces, some embodiments may (1)identify the high heap usage seasons by estimating the seasonal trendsof heap usage statistics of the execution environment and (2) estimate,for each of one or more classes of threads, the seasonal trends of thethread intensity statistics of the class of threads. Some techniques fordetermining the seasonal trends of the heap usage statistics and theseasonal trends of the thread intensity statistics, for regular orirregular time intervals, are disclosed in the patent application Ser.Nos. 14/109,578, 14/109,546, and 14/705,304, which are hereinincorporated by reference for all purposes.

To determine a seasonal trend of a statistic, the period and intervalsto which the seasonal trend is mapped may be defined. In particular, aperiod can be partitioned into a plurality of non-overlapping intervals.Each interval of the period can be associated with a seasonal index. Forexample, if the period is a day and the interval is an hour, then thereshould be 24 seasonal indices to cover the period. As another example,if the period is a year and the interval is a month, there should be 12seasonal indices.

Some embodiments can model the weekdays, weekends, and holidays asseparate periods. If the weekday and weekend periods are separated, thenthere can be 5 cycles of the weekday periods interleaved with 1 cycle ofthe weekend period such that after processing 5 consecutive weekdayperiods, a single weekend period is processed. Accordingly, thefrequency of the consecutive weekday periods will be one weekday periodevery 24 hours while the frequency of the weekend period will be oneweekend period every 7 days. In embodiments where the individualholidays (e.g., the Christmas and New Year Holidays) are modeled asseparate periods, the frequency of a particular holiday period is once ayear.

A seasonal index can be a multiplicative seasonal factor or an additiveseasonal term that is applied to the interval associated with theseasonal index. For example, in an embodiment that represents seasonalindices using multiplicative seasonal factors, if the interval ‘9-LOAM’is associated with a seasonal factor of 1.3, then any measurementsampled during the 9-LOAM interval can be adjusted higher by 30% (i.e.,multiplied by 1.3). In embodiments where seasonal indices arerepresented by additive seasonal terms, the additive seasonal terms areadded to measurements.

A season classifies a set of intervals by some criteria. For example,given a period of one year, the 12 intervals January, February, March,April, May, June, July, August, September, October, November, andDecember can be classified into four northern meteorological seasons asfollows:

December, January, and February are classified as the winter season.

March, April, and May are classified as the spring season.

June, July, and August are classified as the summer season.

September, October, and November are classified as the fall season.

Some embodiments may partition weekday periods into 96 15-minuteintervals. In this regard, 96 seasonal indices are derived, where eachof the 96 weekday seasonal indices (i.e., weekday factors) maps to adifferent one of the 96 weekday intervals. Similarly, some embodimentsmay partition weekend periods into 192 15-minute intervals, therebyderiving 192 seasonal indices with each of the 192 weekend seasonalindices (i.e., weekend factors) mapping to a different one of the 192weekend intervals.

In order to separate out seasonal patterns of the weekday periods andthose of the weekend periods, certain embodiments may apply multi-periodtrending filters to the weekday periods separately from applying suchfilters to the weekend periods. Some embodiments may then renormalizethe weekday factors and the weekend factors so that a seasonal factor of1 represents a common reference level for both the weekday periods andthe weekend periods. As a result, a seasonal factor that is larger than1 may represent a higher than average heap usage during an interval towhich the seasonal factor applies. Meanwhile, another seasonal factorthat is smaller than 1 may represent a lower than average heap usageduring another interval to which the other seasonal factor applies.

In some embodiments, techniques for multi-period trending can beextended to separate out holidays (e.g., Labor Day, Christmas Day, NewYear's Day, etc.) as separate periods, where holidays periods repeatwith a frequency of once every 12 months. Meanwhile, the weekday periodrepeats with a frequency of once every 24 hours and the weekend periodrepeats with a frequency of once every 7 days. In such embodiments, theseasonal factors for holiday periods, the seasonal factors for theweekday periods, and the seasonal factors for the weekend periods mayall be renormalized together so that a seasonal factor of 1 represents acommon reference level for weekday periods, weekend periods, and holidayperiods.

Given a period (e.g., a weekday period, a weekend period, or aholiday/one-year period, etc.), let P denote the number of cycles of theperiod covered by a given measurement dataset (e.g., a time series ofheap usage measurements spanning a particular period of time) and let Kdenote the number of intervals within the number of periods covered bythe given data set. If L denotes the number of seasonal indices in aperiod, then K=P*L. For example, if there are at least 3 years of datawithin the dataset, a period corresponds to a year, and an intervalcorresponds to a month, then the number of available cycles P of theperiod is 3 and the number of available monthly intervals is 36.

Some embodiments may calculate the average heap usage for each intervalof the period based on data spanning multiple cycles of the period. Inparticular, some embodiments may enumerate the intervals from 0 to (K−1)and calculate an average heap usage for each of the enumerated intervalsx _(k) using the following formula:

${{\overset{\_}{x}}_{k} = {\frac{1}{N_{k}}{\sum\limits_{i = 1}^{N_{k}}x_{t_{i}}}}},{k = 0},1,\ldots\mspace{14mu},{{K - 1};N_{k}}$is the number of samples in the interval k;

-   -   and t_(i) is the time of the sample number i in the interval k

Some embodiments may also calculate the average heap usage of each cycleof the period based on the data spanning multiple cycles of the period.In particular, some embodiments may enumerate the cycles of the periodfrom 0 to (P−1) and calculate an average heap usage for each of theenumerated cycles D_(p) of the period using the following formula:

${D_{p} = {\frac{1}{N_{p}}{\sum\limits_{i = 1}^{N_{p}}x_{t_{i}}}}},{p = 0},1,\ldots\mspace{14mu},{{P - 1};}$N_(p) is the number of samples in the cycle p of the period; and t_(i)is the time of the sample number i in the cycle p of the period

To initialize the seasonal factors of a period, some embodiments maycompute the seasonal factors for each of the seasonal indices S _(l) inthe period using the following formula:

${{\overset{\_}{S}}_{l} = {\frac{1}{P}\left( {{{\overset{\_}{x}}_{l}\text{/}D_{0}} + {{\overset{\_}{x}}_{l + L}\text{/}D_{1}} + {{\overset{\_}{x}}_{l + {2 \star L}}\text{/}D_{m}} + \ldots + {{\overset{\_}{x}}_{l + {{({P - 1})} \star L}}\text{/}D_{P - 1}}} \right)}},{l = 0},1,\ldots\mspace{14mu},{L - 1}$

In particular, a seasonal factor for a particular interval may be equalto the ratio of the average heap usage of that interval across theentire dataset (calculated by averaging the average heap usage of all ofthe same intervals (e.g., all 9-10 AM intervals) in the entire dataset(e.g., a dataset that spans an entire week) and the average heap usageof the period across the entire dataset.

C. Renormalization

As mentioned above, some embodiments may renormalize the weekdayseasonal factors and the weekend seasonal factors so that a seasonalfactor of ‘1’ represents a common reference level for both weekdayperiods and weekend periods.

In general, certain embodiments may perform renormalization by computinga weighted average of seasonal factors across all periods and dividingeach of the seasonal factors by the weighted average. Consider thefollowing example involving the seasonal indices of multiple periods ofdiffering lengths, where each period is partitioned into 15 minuteintervals:

seasonal indices for a weekday: D_(i), i=1, 2, . . . 96

seasonal indices for a weekend: E_(i), i=1, 2, . . . , 192

seasonal indices for 10 individual holidays: H_(k,i), i=1, 2, . . . ,96; k=1, 2, . . . 10

Suppose that in a particular year, there are 253 weekdays (excludingholidays), 50.5 weekends, and 10 holidays, where 253+50.5*2+10=364 days.In this example, some embodiments may use the following formula tocalculate the weighted average ‘A’ of the seasonal factors, where theweights are proportional to the number of cycles of each period (e.g.,the weekday period, the weekend period, and 10 individual holidayperiods) in a year.

$A = {\frac{1}{364}\left( {{253{\sum\limits_{i = 1}^{86}D_{i}}} + {50.5{\sum\limits_{i = 1}^{192}E_{i}}} + {10{\sum\limits_{k = 1}^{10}{\sum\limits_{i = 1}^{86}H_{k,i}}}}} \right)}$

Some embodiments can derive the new renormalized seasonal factors foreach period by dividing each seasonal factor D_(i), E_(i), and H_(k,i)by A.

Returning to the steps for identifying the heap-hoarding stack traces,after initializing the seasonal indices S _(l) using the above formulae,some embodiments can renormalize the weekday and weekend factors bydividing each weekend factor B _(k) and each weekday factor C_(l) by anormalization factor as follows:

$\frac{1}{K + {5L}}\left( {{\sum\limits_{k = 0}^{K - 1}{\overset{\_}{B}}_{k}} + {5{\sum\limits_{l = 0}^{L - 1}{\overset{\_}{C}}_{l}}}} \right)$

After renormalization of the weekday and weekend seasonal factors, aseasonal factor of 1 should represent a common reference level for bothweekday factors and weekend factors.

D. Smooth-Spline Fitting

As mentioned above, some embodiments may fit a smooth-spline acrossmultiple periods to provide smooth transitions between the cycles of aperiod (e.g., between two weekday periods) or between the cycles of twoadjacent periods (e.g., between a weekday period and a weekend). Inparticular, fitting a spline can involve concatenating the seasonalindices of one or more periods to smooth transitions between theperiods.

In general, when certain embodiments (e.g., a filter) reach the end ofthe cycle of a period A_(i) and begin a new cycle of the period A_(i),such as when repeating the weekday cycles at the transition from aMonday to a Tuesday, a Tuesday to a Wednesday, a Wednesday to aThursday, and a Thursday to a Friday, such embodiments can concatenatethree sequences of the seasonal indices A_(i) and fit the smooth-splineacross the whole sequence. Some embodiments may then take the middlesegment of the smoothed sequence to represent the new smoothed seasonalindices A_(i).

When certain embodiments (e.g., a filter) reach the end of the cycle ofa period A_(i) and begin a new cycle of an adjacent period B_(i), suchas when transitioning from a Friday to a Saturday, some embodiments mayconcatenate one sequence of the seasonal indices A_(i), one sequence ofthe seasonal indices B_(i), and one sequence of the seasonal indicesC_(i) of a period that follows the period B_(i), and fit thesmooth-spline across the whole sequence. Some embodiments may then takethe middle segment of the smoothed sequence to represent the newsmoothed seasonal indices B_(i). Some embodiments may also take thefirst segment of the smoothed sequence to represent the smoothedseasonal indices A_(i).

When certain embodiments (e.g., a filter) reach the end of the cycle ofa period B_(i) and begin a new cycle of an adjacent period C_(i), suchas when transitioning from a Sunday to a Monday, some embodiments canconcatenate one sequence of the seasonal indices A_(i) of a period thatprecedes the period B_(i), one sequence of the seasonal indices B_(i),and one sequence of the seasonal indices C_(i), and fit thesmooth-spline across the whole sequence. Some embodiments may then takethe middle segment of the smoothed sequence to represent the newsmoothed seasonal indices B_(i). Some embodiments may also take thethird segment of the smoothed sequence to represent the new smoothedseasonal indices C_(i).

With regards to cloud services, load cycles during weekends and holidaysare often different from those during weekdays. Conventional seasonaltrending solutions may typically represent only one period of seasonalindices. In order to separate the seasonal indices of weekends from theseasonal indices of regular weekdays, such conventional solutions maydepend on the range of a period being extended to an entire week or anentire month. Additionally, such conventional solutions may handleholidays separately.

Returning to the steps for identifying the heap-hoarding stack traces,to smooth the weekday seasonal factors, some embodiments can compose anarray of seasonal factors by concatenating three sequences of theweekday factors. For example, some embodiments may generate the array byexecuting the following code in the R programming language:

factors <− c(smoothedWeekdaySeasonalFactor,smoothedWeekdaySeasonalFactor, smoothedWeekdaySeasonalFactor)

Next, some embodiments may apply a spline to smooth out the array of theweekday factors. For example, some embodiments may invoke the Rsmooth.spline function with a smoothing parameter of 0.3 to smooth outthe factors:

extendedWeekdayIndices <− 1:(3 * 96) f <−smooth.spline(extendedWeekdayIndices, factors, spar = 0.3)

Some embodiments may then designate the middle sequence (i.e., themiddle 96 weekday factors) within the array as the smoothed weekdayfactors. For example, some embodiments may obtain the smoothed weekdayfactors by executing the following code in the R programming language:

sandwichWeekdayIndices <− (96 + 1):(96 * 2)smoothedWeekdaySeasonalFactor <− predict(f, sandwichWeekdayIndices)$y

In a fashion similar to smoothing the weekday factors, some embodimentsmay apply a spline to smooth the weekend factors. In particular, someembodiments may compose an array of seasonal factors by concatenating asequence of weekend factors between two sequences of weekday factors.For example, some embodiments may generate the array by executing thefollowing code in the R programming language:

factors <− c(smoothedWeekdaySeasonalFactor,smoothedWeekendSeasonalFactor, smoothedWeekdaySeasonalFactor)

Next, some embodiments may apply a spline to smooth out the array of theweekday and weekend factors. For example, some embodiments may invokethe R smooth.spline function with a smoothing parameter of 0.3 to smoothout the factors:

extendedWeekendIndices <− 1:(2 * 96 + 192) f <−smooth.spline(extendedWeekendIndices, factors, spar = 0.3)

Some embodiments may then designate the middle sequence (i.e., themiddle 192 seasonal factors within the array, which are weekend factors)within the array as the smoothed weekend factors. For example, someembodiments may obtain the smoothed weekend factors by executing thefollowing code in the R programming language:

sandwichWeekendIndices <− (96 + 1):(96 + 192)smoothedWeekendSeasonalFactor <− predict(f, sandwichWeekendIndices)$y

It should be noted that some embodiments may represent the 96 weekdayseasonal indices and 192 weekend seasonal indices separately in order toseparate seasonal patterns observed during weekdays from those observedduring weekends. In some embodiments, sequentially filtering time-seriesof heap usage statistics can involve five sets of exponential filters,including one for heap usage measurements, one for seasonal factors, onefor the linear trend, one for the acceleration trend, and one for theresidual.

As mentioned above, to ensure sample accuracy, heap allocationmeasurements may be taken during full garbage collection (GC) cyclesthat occur at irregular time intervals. In situations where heap usageis especially high, sampling intervals may become arbitrarily close tozero due to constant garbage collecting. Because forecasting involvesestimation of the rate of change, if the irregular time intervals getarbitrarily close to zero, the rate of change may become a randomvariable of Cauchy distribution, whose mean and standard deviation areundefined. Thus, some embodiments may employ the adaptations of Holt'sdouble exponential filter, Winters' triple exponential filter, Wright'sextension for irregular time intervals, Hanzak's adjustment factor fortime-close intervals, and outlier detection and clipping with adaptivescaling of outlier cutoff to overcome the Cauchy distribution problemfor determining the seasonal trends of statistics determined inassociation with full GCs. In some embodiments, the five sets ofexponential filters can be sequentially applied to the times-series toestimate the weekday factors and weekend factors.

When certain embodiments (e.g., a filter) reach the end of a processingcycle for the weekday and weekend period, before processing the nextcycle of the period or transitioning to a different period (e.g.,transition from a weekday period to a weekend period), such embodimentscan divide each weekend factor B _(k) and weekday factor C _(l) by thenormalization factor as follows:

$\frac{1}{K + {5L}}\left( {{\sum\limits_{k = 0}^{K - 1}{\overset{\_}{B}}_{k}} + {5{\sum\limits_{l = 0}^{L - 1}{\overset{\_}{C}}_{l}}}} \right)$

After the end of each period, some embodiments may apply a spline tosmooth the seasonal factors. For instance, when reaching the end of aweekday period that precedes another weekday period (i.e., whentransitioning from a Monday to a Tuesday, a Tuesday to a Wednesday, aWednesday to a Thursday, or a Thursday to a Friday), some embodimentscan compose an array of seasonal factors by concatenating threesequences of the weekday factors. For example, some embodiments maygenerate the array by executing the following code in the R programminglanguage:

factors <− c(smoothedWeekdaySeasonalFactor,smoothedWeekdaySeasonalFactor, smoothedWeekdaySeasonalFactor)

Next, some embodiments may apply a spline to smooth out the array of theweekday factors. For example, some embodiments may invoke the Rsmooth.spline function with a smoothing parameter of 0.3 to smooth outthe factors:

extendedWeekdayIndices <− 1:(3 * 96) f <−smooth.spline(extendedWeekdayIndices, factors, spar = 0.3)

Some embodiments may then designate the middle sequence (i.e., themiddle 96 weekday factors) within the array as the smoothed weekdayfactors. For example, some embodiments may obtain the smoothed weekdayfactors by executing the following code in the R programming language:

sandwichWeekdayIndices <− (96 + 1):(96 * 2)smoothedWeekdaySeasonalFactor <− predict(f, sandwichWeekdayIndices)$y

In a different instance, when reaching the end of a weekday period thatprecedes a weekend period (i.e. when transitioning from a Friday to aSaturday), some embodiments can compose an array of seasonal factors byconcatenating a sequence of weekend seasonal factors between twosequences of weekday seasonal factors. For example, some embodiments maygenerate the array by executing the following code in the R programminglanguage:

factors <− c(smoothedWeekdaySeasonalFactor,smoothedWeekendSeasonalFactor, smoothedWeekdaySeasonalFactor)

Next, some embodiments may apply a spline to smooth out the array of theweekday and weekend factors. For example, some embodiments may invokethe R smooth.spline function with a smoothing parameter of 0.3 to smoothout the factors:

extendedWeekendIndices <− 1:(2 * 96 + 192) f <−smooth.spline(extendedWeekendIndices, factors, spar = 0.3)

Some embodiments may then designate the left sequence (i.e., the first96 seasonal factors within the array, which are weekday factors) withinthe array as the smoothed weekday factors. For example, some embodimentsmay obtain the smoothed weekday factors by executing the following codein the R programming language:

leftsideWeekendIndices <− 1:96 smoothedWeekdaySeasonalFactor <−predict(f, leftsideWeekendIndices)$y

In a different instance, when reaching the end of a weekend period(i.e., transitioning from a Sunday to a Monday), some embodiments cancompose an array of seasonal factors by concatenating a sequence ofweekend seasonal factors between two sequences of weekday seasonalfactors. For example, some embodiments may generate the array byexecuting the following code in the R programming language:

factors <− c(smoothedWeekdaySeasonalFactor,smoothedWeekendSeasonalFactor, smoothedWeekdaySeasonalFactor)

Next, some embodiments may apply a spline to smooth out the array of theweekday and weekend factors. For example, some embodiments may invokethe R smooth.spline function with a smoothing parameter of 0.3 to smoothout the factors:

extendedWeekendIndices <− 1:(2 * 96 + 192) f <−smooth.spline(extendedWeekendIndices, factors, spar = 0.3)

Some embodiments may then designate the middle sequence (i.e., themiddle 192 seasonal factors within the array, which are weekend factors)within the array as the smoothed weekend factors. For example, someembodiments may obtain the smoothed weekend factors by executing thefollowing code in the R programming language:

sandwichWeekendIndices <− (96 + 1):(96 + 192)smoothedWeekendSeasonalFactor <− predict(f, sandwichWeekendIndices)$y

Some embodiments may also designate the right sequence (i.e., the last96 seasonal factors within the array, which are weekday factors) withinthe array as the smoothed weekday factors. For example, some embodimentsmay obtain the smoothed weekday factors by executing the following codein the R programming language:

rightsideWeekendIndices <− (96 + 192+ 1):( 2 * 96 + 192)smoothedWeekdaySeasonalFactor <− predict(f, rightsideWeekendIndices)$y

It should be noted that, some embodiments may execute therenormalization and the smooth-spline fitting described above each timethe sequential filters reach either (1) the end of a cycle of a periodand begin a new cycle of the same period (e.g., the sequential filtersreach the end of a Monday) or (2) the end of a cycle of a period andbegin a new cycle of an adjacent period (e.g., the sequential filtersreach the end of a Friday).

E. Testing for Seasonal Cycles

Some embodiments can test the existence of seasonal cycles for one ormore candidate period of a data set to determine whether a separatesequence of seasonal indices for the period should be represented. Ingeneral, to determine whether a data set exhibits a seasonal cycle of aparticular period, some embodiments may perform the following steps.

Let Q denote the number of seasonal indices in a period, P denote thenumber of available cycles of a period, and K denote the number ofavailable intervals across the cycles of a period, where K=P*Q.

Some embodiments can calculate the average measure in each interval ofthe cycles of a period. To do so, some embodiments may enumerate theintervals from 0 to (K−1) and calculate an average measure of eachinterval of the period using the formula below:

${{\overset{\_}{x}}_{k} = {\frac{1}{N_{k}}{\sum\limits_{i = 1}^{N_{k}}x_{t_{i}}}}},{k = 0},1,\ldots\mspace{14mu},{{K - 1};N_{k}}$is the number of samples in the interval k;

-   -   and t_(i) is the time of the sample number i in the interval k

Some embodiments can then calculate the average measure of each cycle ofthe period. To do so, some embodiments may enumerate the cycles of theperiod from 0 to (P−1) and calculate an average measure of each cycle ofthe period using the formula below:

${D_{p} = {\frac{1}{N_{p}}{\sum\limits_{i = 1}^{N_{p}}x_{t_{i}}}}},{p = 0},1,\ldots\mspace{14mu},{{P - 1};}$

-   -   N_(p) is the number of samples in the cycle p of the period;    -   and t_(i) is the time of the sample number i in the cycle p of        the period

Some embodiments can then compute the sequence Y _(p)=<Y _(p,0), Y_(p,0), . . . , Y _(p,Q−1)> of seasonal indices for each cycle p of theperiod using the formula below:

${{\overset{\_}{Y}}_{p,j} = \frac{{\overset{\_}{x}}_{j}}{D_{p}}},{{j = {k\mspace{14mu}{modulo}\mspace{14mu} Q}};}$k = 0, 1, …  , K − 1 p = 0, 1, …  , P − 1

Some embodiments can then apply null hypothesis testing to detectwhether there are seasonal cycles in the period. In this regard, thenull hypothesis that is to be tested may correspond to the assumptionthat the correlation coefficient r_(u,v) between the seasonal indices ofa most recent cycle ‘u’ and the seasonal indices of a preceding cycle‘v’ is zero. In particular, some embodiments may determine thecorrelation coefficient r_(u,v) using the following formulae below:

${{Mean}\mspace{14mu}\left( {\overset{\_}{Y}}_{p} \right)} = {\frac{1}{Q}{\sum\limits_{j = 0}^{Q - 1}{\overset{\_}{Y}}_{p,j}}}$${{Variance}\mspace{14mu}\left( {\overset{\_}{Y}}_{p} \right)} = {\frac{1}{11}{\sum\limits_{j = 0}^{Q - 1}\left( {{\overset{\_}{Y}}_{p,j} - {{Mean}\mspace{14mu}\left( {\overset{\_}{Y}}_{p} \right)}} \right)^{2}}}$$r_{u,v} = \frac{\sum\limits_{j = 0}^{Q - 1}{\left( {{\overset{\_}{Y}}_{u,j} - {{Mean}\mspace{14mu}\left( {\overset{\_}{Y}}_{u} \right)}} \right)\left( {{\overset{\_}{Y}}_{v,j} - {{Mean}\mspace{14mu}\left( {\overset{\_}{Y}}_{v} \right)}} \right)}}{11\sqrt{{{Variacle}\left( {\overset{\_}{Y}}_{u} \right)}\mspace{14mu}{{Variacle}\left( {\overset{\_}{Y}}_{u} \right)}}}$

Some embodiments may employ various techniques to determine whether thecorrelation coefficient r_(u,v) is large enough to indicate, above alevel of significance, that there is a common seasonal cycle between thecycles ‘u’ and ‘v’. For example, some embodiments may employ theStudent-t test, the permutation test, or the Fisher transformation.

To test the hypothesis, some embodiments may define one or more teststatistics, which may be a function of the parameter. In this case, thecorrelation coefficient r_(u,v) is to be tested. The following teststatistics t has Student's t-distribution, with ‘n−2’ degrees of freedomand is a function of r_(u,v). Some embodiments define the nullhypothesis, r_(u,v)=0, which assumes that the seasonal indices are notcorrelated between the cycles of a period. Some embodiments may searchfor evidence to reject the null hypothesis (i.e., r_(u,v)=0) byaccepting an alternative hypothesis.

$t = {r_{u,v}\sqrt{\frac{n - 2}{1 - r_{u,v}^{2}}}}$

Let F(t) denote the probability distribution. Given the level ofsignificance of 0.1, let t_(0.9,(n−2)) denote the value of the randomvariable t such that F(t)=0.9. The alternative hypothesis is theone-sided condition:

${r_{u,v}\sqrt{\frac{n - 2}{1 - r_{u,v}^{2}}}} > t_{0,{9{({n - 2})}}}$

If this condition is true, the alternative hypothesis is accepted, whichindicates that there is a common seasonal cycle between cycles years ‘u’and ‘v’. If there are common seasonal cycles between the most recentcycle and the preceding cycles, then some embodiments may proceed tocompute the seasonal factors for each of the seasonal indices of thecycle. Some embodiments apply the above formula to detect the existenceof an annual seasonal cycle of the heap usage by the software executionenvironment, as described below.

F. Detecting Annual Seasonal Cycle for Heap Usage

When analyzing multiple years of heap usage statistics of a softwareexecution environment, some embodiments may detect more than oneseasonal trend at different time scales. For example, such embodimentsmay detect, a multi-year time-series of heap usage statistics, a yearlyseasonal trend and a daily seasonal trend, which are both superimposedonto a multi-seasonal trend. Thus, some embodiments may adopt anappropriate time scale to analyze the yearly seasonal trend, where thetime scale has a period correspond to 1 year and an interval correspondto 1 month. As such, the year-long period may be partitioned into 12month-long intervals.

To determine whether the data set exhibits an annual seasonal cycle,some embodiments may first determine multiplicative factors for themonthly indices in the data set.

In a particular instance, let P denote the number of available years(i.e., the number of cycles of the one-year period) in the data set.Additionally, let Q denote the number of available months (i.e., thenumber of intervals within the number of cycles) in the data set.Accordingly, Q=12*P. Let K denote the number of available weekdays orweekends in the data set. Let the index k range from 0 to (K−1) torepresent an enumeration of the available weekdays or weekends. LetN_(k) denote the number of samples in the k^(th) weekday or weekend.Using the following formula, some embodiments can apply the followingformula to calculate the average heap usage of each weekday or weekendin the dataset:

${{\overset{\_}{x}}_{k} = {\frac{1}{N_{k}}{\sum\limits_{i = 1}^{N_{k}}x_{t_{i}}}}},{k = 0},1,\ldots\mspace{14mu},{K - 1}$and N_(k) is the number of samples in the day k

Some embodiments can define a function H, H: (Year×Integer)→Index, whichmaps an ordered pair including the index of the year and an integer thatcorresponds to the index of a weekday or weekend within that year. Usingthe following formula, some embodiments may then calculate the averageheap usage of each year from the average heap usage of the weekdays orweekends within that year:

${{\overset{\_}{Z}}_{p} = {\frac{1}{N_{p}}{\sum\limits_{i = 1}^{N_{p}}{\overset{\_}{x}}_{H{({p,i})}}}}},{p = 0},1,\ldots\mspace{14mu},{{P - 1};}$

-   -   N_(p) is the number of weekdays in the cycle p of the oneyear        period;    -   and H(p, i) is the index of the i^(th) weekday in the cycle p of        the oneyear period.

Some embodiments define a function G, G:(Month×Integer)→Index, whichmaps an ordered pair including the index of the month and an integerthat corresponds to the index of a weekday or a weekend within thatmonth. Using the following formula, some embodiments may calculate theaverage heap usage of each monthly interval of the period from theaverage heap usage of the weekdays or weekends within that month:

${{\overset{\_}{Y}}_{p,m} = {\frac{1}{M_{m}{\overset{\_}{Z}}_{p}}{\sum\limits_{i = 1}^{M_{m}}{\overset{\_}{x}}_{G{({m,i})}}}}},{m = 0},1,\ldots\mspace{14mu},{{Q - 1};}$

-   -   M_(m) is the number of weekdays in the month m;    -   G(m, i) is the index of the i^(th) weekday in the month m;    -   and p is the index of the cycle of the year period.

In particular, the above formula produces Y=<Y _(p,0), Y _(p), . . . , Y_(p,Q)>, which correspond to 12 monthly averages for each cycle of theyear-long period p. The average heap usage for a month can be divided bythe yearly average heap usage to obtain a multiplicative factor for themonthly indice that corresponds to that month. In such embodiments, ifthe multiplicative factor for a particular month is determined to begreater than 1, then the heap usage in that month is above average. Onthe other hand, if the multiplicative factor for a particular month isdetermined to be less than 1, then the heap usage in that month is belowaverage.

After determining the multiplicative factors for the monthly indices,some embodiments can apply null hypothesis testing to detect whetherthere are annual seasonal cycles. In this regard, the null hypothesisthat is to be tested may correspond to the assumption that thecorrelation coefficient r_(u,v) between the monthly indices of the mostrecent year and the monthly indices of a preceding year ‘v’ is zero. Inparticular, some embodiments may determine the correlation coefficientr_(u,v) using the following formulae below:

${{Mean}\left( {\overset{\_}{Y}}_{p} \right)} = {\frac{1}{12}{\sum\limits_{j = 1}^{12}{\overset{\_}{Y}}_{p,j}}}$${{Variance}\left( {\overset{\_}{Y}}_{p} \right)} = {\frac{1}{11}{\sum\limits_{j = 1}^{12}\left( {{\overset{\_}{Y}}_{p,j} - {{Mean}\left( {\overset{\_}{Y}}_{p} \right)}} \right)^{2}}}$$r_{u,v} = \frac{\sum\limits_{j = 1}^{12}{\left( {{\overset{\_}{Y}}_{u,j} - {{Mean}\left( {\overset{\_}{Y}}_{u} \right)}} \right)\left( {{\overset{\_}{Y}}_{v,j} - {{Mean}\left( {\overset{\_}{Y}}_{v} \right)}} \right)}}{11\sqrt{{{Variacle}\left( {\overset{\_}{Y}}_{u} \right)}{{Variacle}\left( {\overset{\_}{Y}}_{v} \right)}}}$

Some embodiments may employ various techniques to determine whether thecorrelation coefficient r_(u,v) is large enough to indicate, above alevel of significance, that there is a common seasonal cycle between theyears ‘u’ and ‘v’. For example, some embodiments may employ theStudent-t test, the permutation test, or the Fisher transformation.

The following test statistics t has Student's t-distribution, with ‘n−2’degrees of freedom, if the null hypothesis is true (i.e., r_(u,v)=0).

$t = {r_{u,v}\sqrt{\frac{n - 2}{1 - r_{u,v}^{2}}}}$

Let F(t) denote the probability distribution. Given the level ofsignificance of 0.1, let t_(0.9,(n−2)) denote the value of the randomvariable t such that F(t)=0.9. The alternative hypothesis is theone-sided condition:

${r_{u,v}\sqrt{\frac{n - 2}{1 - r_{u,v}^{2}}}} > t_{0.9,{({n - 2})}}$

The condition that accepts the alternative hypothesis indicates thatthere is a common seasonal cycle between the years ‘u’ and ‘v’.

G. Determining Annual High Heap Usage Season

If it is determined that there are common seasonal cycles between themost recent year and preceding years, some embodiments can compute theseasonal factors for each month enumerated by the monthly seasonal index0 to 11 by employing the following formula:

${{\overset{\_}{S}}_{n} = {\frac{1}{P}\left( {{\overset{\_}{Y}}_{n} + {\overset{\_}{Y}}_{n + 12} + {\overset{\_}{Y}}_{n + {2*12}} + \ldots + {\overset{\_}{Y}}_{n + {{({P - 1})}*12}}} \right)}},{n = 0},1,\ldots\mspace{14mu},11$

In an alternative embodiment, the monthly indices Y _(p) of the mostrecent year (i.e., cycle) can be used as the monthly seasonal indices,as indicated by the following formula:S _(n) =Y _(p,n) , n=0,1, . . . ,11

To classify the annual high heap usage season, some embodiments canidentify the seasonal index N corresponding to the month that has thelargest seasonal factor in the year-long period. Such embodiments canthen use the index N as a seed. Starting from N, such embodiments canscan the seasonal indices less than or greater than N (i.e., seasonalindices 0, 1, 2 . . . N−1, N+1, N+2) that have seasonal factors greaterthan a threshold T. In some embodiments, T is greater than 1. Someembodiments may classify more than one disjoint high heap usage seasonif there is more than one N such that S _(N)=MAX(S _(n)). The functionMAX (S _(n), s) selects the s^(th) element of a sequence of indices N, S_(N)=MAX(S _(n)). The parameters is used to break the tie in case thereis more than one N such that S _(N)=MAX(S _(n)). Some embodiments mayclassify each disjoint high heap usage season and repeat the correlationanalysis for each season. In some embodiments, a method to classify theset of monthly seasonal indices for a high heap usage season is definedby the following recursion:

$\mspace{20mu}{V_{0} = \left\{ {\left. N \middle| {\overset{\_}{S}}_{N} \right. = {{MAX}\left( {{\overset{\_}{S}}_{n},s} \right)}_{{n = 0},\ldots\mspace{14mu},{({p - 1})}}} \right\}}$$V_{W + 1} = {V_{W}\bigcup\left\{ J \middle| {{\overset{\_}{S}}_{J} > {T\mspace{14mu}{{and}\mspace{14mu}\left\lbrack {\left\lbrack {{J = {\left( {K + 1} \right){mod}\mspace{14mu} P}},{K = {{MAX}\left( V_{W} \right)}}} \right\rbrack\mspace{14mu}{{or}\mspace{14mu}\left\lbrack {{J = {\left( {L - 1 + P} \right)\mspace{14mu}{mod}\mspace{14mu} P}},{L = {{MIN}\left( V_{W} \right)}}} \right\rbrack}} \right\rbrack}}} \right\}}$$\mspace{20mu}{V = {\bigcup\limits_{W = {0\mspace{14mu}\ldots\mspace{14mu}{({P - 1})}}}V_{W}}}$

It should be noted that the above recursion involves an unbound variables that can be used to break a tie. In some embodiments, s=1 by default.

In certain embodiments, the closure V of the seasonal indices classifiesan annual high heap usage season. The threshold T can be set to apercentage, such as 85 percent of the range of the seasonal factors. Forexample, suppose the seasonal factors for the 12 monthly seasonalindices in one year-long period are as given in the following table.

January February March April May June July August September OctoberNovember December 0.76 0.82 1.0 1.2 1.29 1.34 1.26 1.12 1.01 0.99 0.950.9

The range of the multiplicative seasonal factors is (1.34−0.76), whichis 0.58. Accordingly, 85 percent of the range of the seasonal factors is(0.76+0.85*0.58), which is 1.253. Given the 85 percent threshold T,T=1.25. As a result, such embodiments may classify May, June, and Julyas the annual high heap usage season.

Some embodiments can select a segment of the dataset that spans the mostrecent cycle of the year-long period. For example, among the cycles:2013, 2014, 2015, and 2016, such embodiments may select the segment ofdata covering 2015 to 2016. The selected data segment can span 2 or moreweeks of heap usage statistics that are inside the annual high heapusage season. For example, if the seasonal factors are as given in thefollowing table, the data segment can be selected from November 2015,December 2015, and January 2016.

January February March April May June July August September OctoberNovember December 1.26 1.12 1.01 0.99 0.95 0.9 0.76 0.82 1.0 1.2 1.291.34

H. Regression for Filter Constants and Time Zone Offset

Some embodiments can incorporate an estimate of a time zone offset. If atime zone offset is not available, some embodiments can perform anon-linear regression for a segment of the data set to estimate the timezone offset and use it for filtering the data. By providing anestimation of the time zone offset, some embodiments can improve theestimation of the seasonal indices in the transitions between theperiods.

In particular, some embodiments can perform a non-linear regression withthe filter constants (i.e., regression parameters, which are independentvariables): measureFilterConstant α, rateFilterConstant β,accelerationFilterConstant κ, seasonalFactorFilterConstant γ,errorResidualFilterConstant δ, and timeZoneOffset tz to minimize themean square error (MSE) and/or the mean absolute deviation (MAD) of theresidual of the 1-step forecasts. In some embodiments, the time stampsmay be shifted by the time zone offset tz in the regression. Someembodiments may apply a non-linear multivariate regression using anoptimization routine (e.g., the optim routine provided by the Rprogramming language). Some embodiments may derive the weekday andweekend seasonal factors using the optimal values of α, β, κ, γ, δ, andtz, as indicated in the following formulae employed by such embodiments:

${MSE} = {{f\left( {\alpha,\beta,\kappa,\gamma,\delta,{tz},x_{t}} \right)} = \left( {\frac{1}{N}{\sum\limits_{n = 1}^{N}\left( e_{h,t_{n}} \right)^{2}}} \right)^{1/2}}$${MAD} = {{f\left( {\alpha,\beta,\kappa,\gamma,\delta,{tz},x_{t}} \right)} = {\frac{1}{N}{\sum\limits_{n = 1}^{N}{e_{h,t_{n}}}}}}$

Some embodiments include the time zone offset as a regression parameterso that the transitions between cycles of a period or between twoadjacent periods can be as accurate as possible.

I. Ranking Classes of Threads by Degree of Correlation

Once the annual high heap usage season has been determined, someembodiments may calculate and/or obtain weekday/weekend factors thatrepresent daily/weekly seasonal cycles covered by a recent (e.g., mostrecent) annual high heap usage season. It should be noted that thedaily/weekly seasonal cycles in this segment of the data set (i.e.,during an annual high heap usage season) may be more pronounced than atother times (i.e., outside the annual high heap usage season). Thus, thedetermination of degrees of correlation between seasonal trends in heapusage and seasonal trends in the intensity statistics of one or moreclasses of threads may be based on this segment of the data set. Statedanother way, for correlation analysis, some embodiments can derive theseasonal trends of various classes of threads using the same timeintervals as the time intervals covered by the most recent annual highheap usage season.

It should be noted that to determine seasonal trends for the intensitystatistics of a particular class of threads, some embodiments may employtechniques that were used for determining seasonal trends in heap usage,as described above. In other words, seasonal trending of threadintensity statistics and heap usage statistics may both involve usingthe same number of seasonal indices for the weekday and weekend periods(e.g., 96 seasonal indices for a weekday period and 192 seasonal indicesfor a weekend period).

Upon determining the seasonal trends for heap usage and the seasonaltrends of intensity statistics for one or more classes of threads, someembodiments may then compute, for each of the one or more classes ofthreads, the degree of correlation between the seasonal trends for heapusage and the seasonal trends for the intensity statistics of the classof threads. In particular, the degree of correlation may be computed forthe sequences of the 96 seasonal factors or the 192 seasonal factors. Itshould be noted that computing the degree of correlation betweenseasonal trends may be more efficient than computing a degree ofcorrelation between a sequence of heap usage measures and a sequence ofthread intensity measures because sequences of measures may be muchlonger.

Let H denote a sequence of N seasonal factors for heap usage. Let Tdenote a sequence of N seasonal factors for the thread intensity of aclass of threads. The correlation coefficient of the two sequences ofseasonal factors is given by CorrelationCoefficient(H,T), as definedbelow:

${{Mean}(H)} = {\frac{1}{N}{\sum\limits_{j = 1}^{N}H_{j}}}$${{Mean}(T)} = {\frac{1}{N}{\sum\limits_{j = 1}^{N}T_{j}}}$${{Variance}(H)} = {\frac{1}{N - 1}{\sum\limits_{i = 1}^{N}\left( {H_{i} - {{Mean}(H)}} \right)^{2}}}$${{Variance}(T)} = {\frac{1}{N - 1}{\sum\limits_{i = 1}^{N}\left( {T_{i} - {{Mean}(T)}} \right)^{2}}}$${{CorrelationCoeefficient}\left( {H,T} \right)} = \frac{\sum\limits_{i = 1}^{N}{\left( {H_{i} - {{Mean}(H)}} \right)\left( {T_{i} - {{Mean}(T)}} \right)}}{\left( {N - 1} \right)\sqrt{{{Variacle}(H)}{{Variacle}(T)}}}$

Some embodiments may derive weekday and weekend seasonal factors forheap usage by taking a regression of the heap usage statistics includedin the most recent annual high heap usage season. Let's denote the timeinterval of this segment of the data set by (t1, t2). To analyze thecorrelation between the seasonal factors for the intensity statistics ofa class of threads with the seasonal factors for the heap usage, someembodiments can take the seasonal factors from the same time interval(t1, t2) in the seasonal factor time-series in the SeasonalTrendInfoassociated with the class of threads. In particular, the seasonal factortime-series can be stored in the smoothedWeekdaySeasonalFactor membervariable and the smoothedWeekendSeasonalFactor member variable in theassociated SeasonalTrendingInfo object.

Some embodiments can iterate over the ThreadClassificationInfo objectsof all of the classes of threads and recursively traverse theSegmentInfo objects in each of the ThreadClassificationInfo object tocollect SeasonalTrendInfo objects contained within theThreadClassificationInfo objects and the SegmentInfo objects. Incomputing a CorrelationCoefficient(H,T) between the heap usage and eachof the classes of threads using the formulae identified above, someembodiments can retrieve the weekday factors or the weekend factors ineach of the SeasonalTrendInfo objects. Once a degree of correlation hasbeen calculated for each class of thread, some embodiments may rank theclasses of the threads by their degrees of correlation with heap usageseasonal trends. The top ranking classes of threads may then beclassified as heap-hoarding classes of threads. Some embodiments maythen analyze stack traces and code associated with the heap-hoardingclasses of threads to identify inefficient memory usage that can berectified and/or improved, either manually or automatically.

It should be noted that some embodiments can be extended to determinecorrelation coefficients based on periods other than weekday and weekendperiods (e.g., end-of-quarter periods).

FIG. 9 illustrates a flowchart 900 of a process for identifying codethat is likely to be contributing to high heap usage within a softwareexecution environment according to some embodiments. In someembodiments, the process depicted in flowchart 900 may be implemented bya computer system with one or more processors (e.g., computer system1700 of FIG. 17) where the one or more processors can execute the stepsbased on computer code stored in a computer-readable medium. The stepsdescribed in FIG. 9 can be performed in any order and with or withoutany of the other steps.

Flow chart 900 begins at step 902, where embodiments determine a lengthof time when heap usage by one or more processes exceeds a threshold.The length of time may correspond to the annual high heap usage seasonwhile the threshold may correspond to a percentage of the range ofseasonal factors assigned to intervals (e.g., 15 minute intervals)across one or more periods (e.g., the weekday period and the weekendperiod). In some embodiments, the threshold may be set by choosing apercentage. Once the percentage is chosen, the threshold may be given bythe sum of the smallest seasonal factor and the product of the range ofseasonal factors and the percentage. For example, if the chosenpercentage is 85 percent, the smallest seasonal factor is 0.76, and thelargest seasonal factor is 1.34, the threshold may be given by(0.76+0.85*(1.34−0.76)), which 1.253. As a result, any interval with amultiplicative seasonal factor that exceeds 1.25 may be determined to bepart of the length of time when heap usage exceeds the threshold.

At step 904, embodiments determine heap information of the one or moreprocesses during the length of time. The heap information may correspondto the amount of heap memory being used by the one or more processeswithin a software execution environment at different points during thelength of time. For example, the heap information may be based on heapusage measurements obtained from the software execution environment atirregular intervals (e.g., during full GCs). Additionally, the softwareexecution environment may correspond to a production environment thatcomprises one or more virtual machines (e.g., JVMs) and the one or moreprocesses may support one or more cloud services.

At step 906, embodiments determine thread information of the one or moreprocesses during the length of time. In some embodiments, the threadinformation may comprise, for each of one or more classes of threadsdetermined from analyzed thread dumps, a thread intensity seasonalfactor for each of the plurality of intervals.

In some embodiments, the heap information may include a heap usageseasonal factor for each of the plurality of intervals. In particular,the length of time may span one or more cycles of a first period havinga first length (e.g., the weekday period) and one or more cycles of asecond period having a second length (e.g., the weekend period). Eachperiod may be split into a plurality of intervals. For example, theweekday period may be split into 96 15 minute intervals while theweekend period may be split into 192 15 minute intervals.

It should be noted that each of the plurality of intervals may be mappedto a particular season (i.e., seasonal indice) of one of the periods.For each seasonal indice, some embodiments may determine a heap usageseasonal factor and, for each class of thread that is determined, athread intensity seasonal factor, which may result in each intervalbeing associated with a heap usage seasonal factor and a plurality ofthread intensity seasonal factors (one for each class of threads). Forexample, assuming three different classes of threads are discovered, theweekday period may have 96 heap usage seasonal factors and 288 threadintensity seasonal factors (96 thread intensity seasonal factors foreach of the three classes of threads) while the weekend period may have192 heap usage seasonal factors and 576 thread intensity seasonalfactors.

At step 908, embodiments correlate the heap information with the threadinformation to identify one or more lines of code of the one or moreprocesses that correspond to the heap usage exceeding the threshold. Thesteps of correlating the heap information with the thread informationare discussed in further detail below with respect to FIG. 10.

At step 910, responsive to identifying the one or more lines of code,embodiments initiate one or more actions associated with the one or morelines of code. For example, embodiments may generate an alert associatedwith the one or more lines of code that is sent to relevant personnel ora code optimization tool. In response, the identified lines of code maybe investigated and/or optimized. Alternatively, some embodiments mayoptimize the one or more lines of code to use heap memory in a moreefficient fashion.

FIG. 10 illustrates a flowchart 1000 of a process for calculating ofdegrees of correlation between various classes of threads and high heapusage according to some embodiments. In some embodiments, the processdepicted in flowchart 1000 may be implemented by a computer system withone or more processors (e.g., computer system 1700 of FIG. 17) where theone or more processors can execute the steps based on computer codestored in a computer-readable medium. The steps described in FIG. 10 canbe performed in any order and with or without any of the other steps.

Flowchart 1000 begins at step 1002, where embodiments obtain one or morethread dumps of one or more processes. As mentioned above, a controlsystem may periodically cause the software execution environment to takethread dumps, where each thread dump comprises one or more stack tracesof threads spawned by one or more processes executing within thesoftware execution environment.

At step 1004, embodiments obtain one or more classes of threads byreceiving one or more threads from one or more thread dumps andclassifying each of the received threads based on a stack trace thatcorresponds to the received thread. Once all of the thread dumps havebeen received and processed, embodiments may analyze each of the one ormore classes of threads to determine a degree of correlation betweeneach of the classes of threads and high heap usage in steps 1006-1016.

At decision 1006, embodiments determine whether there is another classof threads of the one or more classes of threads to determine a degreeof correlation with high heap usage. If so, embodiments may proceed tostep 1008. Otherwise, embodiments may proceed to step 1018.

At optional step 1008, embodiments calculate a mean of the heap usageseasonal factors of the plurality of intervals. At step 1010,embodiments calculate a mean of the thread intensity seasonal factors ofthe class of threads and of the plurality of intervals. At optional step1012, embodiments calculate a variance of the heap usage seasonalfactors of the plurality of intervals. At step 1014, embodimentscalculate a variance of the thread intensity seasonal factors of theclass of threads and of the plurality of intervals. At step 1016,embodiments calculate the degree of correlation between the class ofthreads and the heap usage exceeding the threshold.

At step 1018, embodiments select, from the one or more classes ofthreads, a given class of threads that has a highest degree ofcorrelation to the heap usage exceeding the threshold. In particular,once a degree of correlation has been calculated for each class ofthread, some embodiments may rank the classes of the threads by theirdegrees of correlation with heap usage seasonal trends. The top rankingclass of threads may then be selected as the given class of threads.

At step 1020, embodiments identify, based on the given class of threads,one or more lines of code that are likely to be contributingsignificantly to high heap usage. In particular, some embodiments maythen analyze file names and lines specified by stack traces to locatelines of code associated with the heap-hoarding classes of threads. Itshould be noted that each thread of the one or more processes thatbelongs to the given class of threads executes the one or more lines ofcode.

VI. Overcoming Weak-Exogeneity and Heteroscedasticity in Forecasting

As mentioned above, to ensure sample accuracy, heap allocationmeasurements may be taken during full garbage collection (GC) cyclesthat occur at irregular time intervals. In situations where heap usageis especially high, sampling intervals may become arbitrarily close tozero due to constant garbage collecting. As a result, time-series databased on the heap allocation measurements may exhibit weak-exogeneity,where the process of generating the residual is somewhat dependent onthe process of generating the time-intervals of full GC samples, andheteroscedasticity, where the variance of the residual is not constantover time.

Conventionally, generating an ordinary least-squares regression of alinear trend assumes that the predictor variable and the responsevariable are generated by a process that is both exogenous andhomoscedastic. However, with regards to a data set based on measurementstaken during full GCs, the predictor variable (i.e., the irregular timeintervals) and the response variable (i.e., the heap usage measurementstaken during a full GC) are not independent because the frequency atwhich full GCs are taken may increase when heap usage increases. Someembodiments may use robust and resistant regression methods to overcomethe weak-exogeneity and heteroscedasticity of the data set.

Certain embodiments may utilize robust least-squares regression toovercome the weak-exogeneity and heteroscedasticity exhibited in suchdata sets. In particular, some embodiments may (1) decompose atime-series of measurements into a de-seasonalized measure component(i.e., a de-seasonalized component) and a seasonal factor component(i.e., a seasonal effector), (2) apply a robust linear regression to thede-seasonalized measure component, (3) apply a smooth-spline filter tothe seasonal factor component, and (4) reconstitute the linearregression line and the smoothed seasonal factors into a seasonal andlinear trend model.

The least-trimmed squares (LTS) estimator is a robust regressiontechnique that is resistant to the influence of outliers. Given a set ofN samples, the LTS estimator minimizes the sum of the smallest 50% ofsquared residuals by trimming out 50% of samples corresponding to thelargest squared residuals as outliers. The LTS estimator runs oneiteration of ordinary least-square regression of all N samples to sortthe residuals to select the smallest N/2 residuals (i.e., trimmedsamples). The LTS estimator then iteratively reruns the regressions byupdating the trimmed samples to reduce the mean of the squaredresiduals. In comparison with certain embodiments described below,however, the time-complexity of the LTS algorithm may be relativelyhigh.

The generalized weighted least-squares (WLS) estimator is a robustregression technique that multiplies the squared error residual of eachsample by a weight that is inversely proportional to the variance of thesample. Employing the WLS estimator may depend on the weights beingdetermined by prior knowledge of the data. For example, the priorknowledge may specify (1) the accuracy of the different instruments usedto measure different sample points, (2) the variance among the redundantmeasurements corresponding to the same time instant, or (3) the varianceamong the nearest neighbor group of measurements. If the weights cannotbe determined by prior knowledge, the WLS estimator may run oneiteration of the ordinary least-squares regression to estimate theresiduals and use the inverse of the residuals as the weights toiteratively rerun the regression to produce a stable estimate of thelinear model. In comparison with certain embodiments described below,however, the time-complexity of the WLS algorithm is relatively high.

In the patent application Ser. No. 14/109,546, which is incorporated byreference herein for all purposes, a set of equations to filter the rateof change r_(t) _(n) of the measure is disclosed. This filter monitorsthe trend of the measure:

$r_{t_{n}} = \frac{x_{t_{n}} - x_{t_{n - 1}}}{t_{n} - t_{n - 1}^{\prime}}$${\overset{\_}{R}}_{t_{n}} = {{v_{t_{n}}r_{t_{n}}} + {\left( {1 - v_{t_{n}}} \right){\overset{\_}{G}}_{t_{n}}}}$

Since the rate of change

$r_{t_{n}} = \frac{x_{t_{n}} - x_{t_{n - 1}}}{t_{n} - t_{n - 1}^{\prime}}$involves a division by the length of time interval (t_(n)−t′_(n−1)),some embodiments may adjust the filter parameter to give a relativelysmall weight to a sample when the length of time interval t_(n)−t′_(n−1)is relatively short.

The filter parameter v_(t) _(n) is adjusted by the adjustment factorsσ_(n) ^(n−1) in the following equations:

$v_{t_{n}} = \frac{v_{t_{n - 1}}}{v_{t_{n - 1}} + {\sigma_{n}^{n - 1}b_{n}}}$b_(n) = (1 − β)^((t_(n) − t_(n − 1)))$\sigma_{n}^{n - 1} = \left( \frac{t_{n - 1} - t_{n - 2}^{\prime}}{t_{n} - t_{n - 1}^{\prime}} \right)$

The rate filter parameter is used to filter the smoothed rate of changeas follows. If seasonal trending is not employed, some embodiments mayuse the value r′_(t) _(n) to update the average, as shown in the formulabelow:R _(t) _(n) =v _(t) _(n) r′ _(t) _(n) (1−v _(t) _(n) ) G _(t) _(n)

On the other hand, if seasonal trending is employed, some embodimentsmay use one of the following formulae depending on whether the timesfall in a weekend or on a weekday period, where B _(τ) _(n) and C _(τ)_(n) are the seasonal factors of weekend and weekday periods,respectively.

${\Delta\; x_{t_{n}}^{\prime}} = \left\{ \begin{matrix}{{\frac{x_{t_{n}}^{\prime}}{{\overset{\_}{B}}_{\tau_{n}}} - \frac{x_{t_{n - 1}}}{{\overset{\_}{B}}_{\tau_{n - 1}}}},} & {t_{n - 1}\mspace{14mu}{and}\mspace{14mu} t_{n}\mspace{14mu}{fall}\mspace{14mu}{in}\mspace{14mu}{the}\mspace{14mu}{weekend}\mspace{14mu}{season}} \\{{\frac{x_{t_{n}}^{\prime}}{{\overset{\_}{C}}_{\tau_{n}}} - \frac{x_{t_{n - 1}}}{{\overset{\_}{C}}_{\tau_{n - 1}}}},} & {t_{n - 1}\mspace{14mu}{and}\mspace{14mu} t_{n}\mspace{14mu}{fall}\mspace{14mu}{in}\mspace{14mu}{the}\mspace{14mu}{weekday}\mspace{14mu}{season}} \\{{\frac{x_{t_{n}}^{\prime}}{{\overset{\_}{B}}_{\tau_{n}}} - \frac{x_{t_{n - 1}}}{{\overset{\_}{C}}_{\tau_{n - 1}}}},} & {t_{n - 1}\mspace{14mu}{falls}\mspace{14mu}{on}\mspace{14mu} a\mspace{14mu}{weekday}\mspace{14mu}{and}\mspace{14mu} t_{n}\mspace{14mu}{falls}\mspace{14mu}{in}\mspace{14mu} a\mspace{14mu}{weekend}} \\{{\frac{x_{t_{n}}^{\prime}}{{\overset{\_}{C}}_{\tau_{n}}} - \frac{x_{t_{n - 1}}}{{\overset{\_}{B}}_{\tau_{n - 1}}}},} & {t_{n - 1}\mspace{14mu}{falls}\mspace{14mu}{in}\mspace{14mu} a\mspace{14mu}{weekend}\mspace{14mu}{and}\mspace{14mu} t_{n}\mspace{14mu}{falls}\mspace{14mu}{on}\mspace{14mu} a\mspace{14mu}{weekday}}\end{matrix} \right.$

Next, some embodiments may determine the deseasonalized raw growth rateusing the following formula:

t n ′ = Δ ⁢ ⁢ x t n ′ t n - t n - 1 ′

Some embodiments may then update the moving average using the formula:R _(t) _(n) =v _(t) _(n)

′_(t) _(n) (1−v _(t) _(n) ) G _(t) _(n)

In particular, a rate filter parameter v_(t) _(n) generated by the aboveequations represents a weight that is based on the length of the timeinterval that occurred in between the particular sample and anothersample immediately previous to the particular sample. There is aone-to-one correspondence between the rate filter parameter and themeasurement data in the time series. FIG. 11 depicts a graph that plotsthe filter parameter v_(t) _(n) against the sampling time intervalacross the whole time range for an example data set. While the timerange is divided into 6 overlapping sub-ranges, the graph in eachsub-range shows that there is a linear relation between the sample timeinterval and the filter parameter. As can be seen in the graph, thefilter parameter (i.e., the weight for the sample) is small when thesample time interval is small. This adjustment dynamically reduces theweight of the samples in the filter depending on the density of thesample points around the current sample point.

Some embodiments use the rate filter parameter to trim the data points.Trimming the data points can help to even out the density of the samplepoints across the whole time range and thus improve the robustness ofthe linear regression algorithm. With regards to the data points thatrepresent the measurements of heap usage in a software executionenvironment during full GC cycles, data points that are close togethermay correspond to a period of higher heap usage (e.g., during loadspikes) where full GCs are performed more often.

Some embodiments compare a rate filter parameter against a threshold andexclude (i.e., trim) the corresponding data point from the robust linearregression if the rate filter parameter is smaller than the threshold.Some embodiments can use the median or mean of the rate filterparameters as a threshold. In particular, some embodiments can trim thedata points that are close together as such data points may representthe load surges or outliers. As a result, some embodiments may alleviatethe weak-exogeneity condition by evening out the density of the datapoints along the time axis, which reduces the correlation between theirregular time-intervals and the residuals.

The time series D _(t) _(n) for the forecast error residual and F _(t)_(n) for the forecasted measure generated by the following equations aredisclosed in the patent application Ser. No. 14/109,546, which isincorporated by reference herein for all purposes.

${\overset{\_}{F}}_{t_{n}} = \left\{ \begin{matrix}{{\overset{\_}{X}}_{t_{n - 1}} + {{\overset{\_}{M}}_{t_{n - 1}}\left( {t_{n} - t_{n - 1}} \right)}} \\{\left\lbrack {{\overset{\_}{X}}_{t_{n - 1}} + {{\overset{\_}{M}}_{t_{n - 1}}\left( {t_{n} - t_{n - 1}} \right)}} \right\rbrack{\overset{\_}{C}}_{\tau_{n} - L}} \\{x_{t_{n - 1}} + {{\overset{\_}{R}}_{t_{n - 1}}\left( {t_{n} - t_{n - 1}} \right)}}\end{matrix} \right.$

Some embodiments may generate the error residual of the forecastedmeasure using the following formula:e _(t) _(n) =F _(t) _(n) −x _(t) _(n)Ē _(t) _(n) =ψ_(t) _(n) e _(t) _(n) +(1−ψ_(t) _(n) )Ē _(t) _(n−1)D _(t) _(n) =ψt _(n) |e _(t) _(n) |+(1−ψ_(t) _(n) ) D _(t) _(n−1)

Because there is a correlation between the smoothed absolute errorresidual D _(t) _(n) generated by the filter and the variance of theresidual of the least-squares regression, some embodiments may use theinverse of the smoothed absolute error residual 1/D _(t) _(n) as theweight for the generalized weighted least-squares regression. In doingso, some embodiments may alleviate the heteroscedasticity condition bygiving a relatively small weight to a sample value that has a relativelylarge deviation from the expected value. The expected value canrepresent a convolution of the near-neighbor group of samples.

The following example code (written in the R programming language) showshow a trimmed subset of the samples and the weights of the samples canbe computed. As shown in the example code below, some embodiments mayuse the R function “rlm”, which enables certain embodiments to specifythe trimmed subset of the samples and the weights of the samples forgenerating a weighted least-squares regression. It should be noted thatthe rateFilterParameter, seasonalFactor, absoluteErrorResidual, measure,and time vectors in the example code are time-series with the same timerange.

trimmingParameter <− c(rateFilterParameter, which(normSeasonalFactor <1.0)) threshold1 <− median(trimmingParameter, na.rm = TRUE) threshold2<− median(rateFilterParameter, na.rm = TRUE) threshold3 <−mean(rateFilterParameter, na.rm = TRUE) trimmingThreshold <−max(threshold1, threshold2, threshold3) lengthOfTimmingParameter <−length(trimmingParameter) # can set up a list of graduated thresholds togive less weight to older data listOfTrimmingThresholds <−c(trimmingThreshold * 1.1, trimmingThreshold * 1.05, trimmingThreshold,trimmingThreshold * 0.95, trimmingThreshold * 0.9)numberOfTrimmingThresholds <− length(listOfTrimmingThresholds) # selectthe exclusion set of the data points which are time close together # mayuse graduated thresholds to give less weight to older data for what is #known as discounted least-squares regression prevSplitPoint <− 0 for(num in 1:numberOfTrimmingThresholds) { splitPoint <−trunc(lengthOfTimmingParameter * num / numberOfTrimmingThresholds)excludeIndices <− c(excludeIndices,which(rateFilterParameter[(prevSplitPoint + 1):splitPoint] <listOfTrimmingThresholds[num]) + prevSplitPoint) prevSplitPoint <−splitPoint } includeIndices <− 1:length(rateFilterParameter)includeIndices <− includeIndices[−excludeIndices] # use the inverseabsolute error residual for weights minErrorResidual <−min(absoluteErrorResidual) if (minErrorResidual == 0) {absoluteErrorResidual[absoluteErrorResidual == 0] <− 1.0minErrorResidual <− 1.0 } weights <− (minErrorResidual /absoluteErrorResidual) # use regression methods robust toheteroscedasticity and weak-exogeneity # use trimmed indices“includeIndices” to compensate for the weak-exogeneity # use weights tocompensate for the heteroscedasticity # in generalized weightedleast-squares linear <− tryCatch(rlm(measure ~ time, weights = weights,method = ″M″, subset = includeIndices), error = function(e)return(null))

The rate filter parameter is given as a time-series of values denoted byv_(t) _(n) for each timestamp t_(n) corresponding to the timestamp ofthe data point. If v_(t) _(n) <z, where z is a threshold, then thecorresponding data point x_(t) _(n) is excluded from the linearregression. Generally, some embodiments can use any value at theN-percentile (e.g., the median, which is the 50-percentile) of the ratefilter parameters as the threshold z.

In some embodiments, the absolute error residual is given as atime-series D _(t) _(n) for each timestamp t_(n) corresponding to thetimestamp of the data point. The weight W_(t) _(n) of the sample attimestamp t_(n) can be inversely proportional to D _(t) _(n) . Someembodiments can compensate for the variance changes among the datapoints that represent the short-term load surges or outliers.

To decrease the influence of outliers and short-term surges in heapusage on the linear regression, some embodiments may combine thetechnique of evening out the density of data points with the techniqueof assign smaller weights to deviating samples values. In doing so, someembodiments may increase the robustness of the linear regression, whichmay facilitate the capturing of long-term trends (e.g., in heap usage).It should be noted that using the two techniques together may provide abetter fit of the linear regression line to the data and may be moreefficient than using conventional an LTS estimator or an WLS estimator,which generally involves several iterations of regression.

To further improve the robustness of the regression, some embodimentsmay additionally identify the transient states and remove the samplepoints that fall in the transient states and remove run-to-run segmentsthat are outliers (e.g., data segments that correspond to the softwareexecution environment experiencing a memory leak, an out of memoryevent, or a very high growth rate)

FIG. 12 displays three trend graphs each derived by a different linearregression technique for the heap usage in a production environment. Theblue color trend line 1205 can be derived by standard linear regressionalgorithm that assigns equal weights to each sample point. The browncolor trend line 1210 can be derived by a conventional robust regressionalgorithm. The red color line 1215 represents a regression provided by apresent embodiment described above, which lies close to the brown colortrend line.

FIG. 13 displays an additional graph that illustrate how a conventionalregression technique may provide incorrect results. As shown in thegraph, the brown color trend line 1305, which represents a conventionalregression technique, fits closely to the two clusters of high densitysample points. In contrast, the red color line 1215 correctly traces thetrend in the sample points to provide a long term projection of the heapusage in the software execution environment.

FIG. 14 illustrates a flowchart 1400 of a process for generating of aforecast of a signal according to some embodiments. In some embodiments,the process depicted in flowchart 1400 may be implemented by a computersystem with one or more processors (e.g., computer system 1700 of FIG.17) where the one or more processors can execute the steps based oncomputer code stored in a computer-readable medium. The steps describedin FIG. 14 can be performed in any order and with or without any of theother steps.

Flowchart 1400 begins at step 1402, where embodiments receive a signalcomprising a plurality of measures sampled over a span of time from anenvironment in which one or more processes are being executed. In someembodiments, the plurality of measures may be heap usage measurementstaken by a control system that is monitoring heap usage within asoftware execution environment (e.g., a production environment), wherethe software execution environment includes one or more executingprocesses.

At step 1404, embodiments extract a seasonal effector and ade-seasonalized component from the signal 1404. In some embodiments, theseasonal effector may correspond to the seasonal factors determined foreach interval of the period assigned to the data set. In someembodiments, the de-seasonalized component may be obtained by applyingthe seasonal factors to the signal.

At step 1406, embodiments apply one or more spline functions to theseasonal effector to generate a first model. In this regard, someembodiments may give relatively small weights to sample values thatdeviate drastically from the expected value, where the expected valuerepresents a convolution of the near-neighbor group of samples.

At step 1408, embodiments apply a linear regression technique to thede-seasonalized component to generate a second model. In particular, tocompensate for relatively short time intervals experienced during highheap usage, some embodiments may adjust a filter parameter to give arelatively small weight to a sample taken during a short interval. Someembodiments may use a rate filter parameter to trim the data pointsincluded in the data set. Trimming the data points can help to even outthe density of the sample points across the whole time range and thusimprove the robustness of the linear regression algorithm.

At step 1410, embodiments generate a forecast of the signal based on thefirst model and the second model. In some embodiments, the forecast ofthe signal may correspond to a regression line that is generated usingthe techniques described in steps 1406 and 1408. In particular, thegenerated forecast may have a better fit to the signal.

At step 1412, embodiments initiate, based at least in part on theforecast, one or more actions associated with the environment. Forexample, if the forecast indicates that heap usage will increase in thefuture, some embodiments may allocate additional resources (e.g.,memory, RAM) to the software execution environment.

FIG. 15 depicts a simplified diagram of a distributed system 1500 forimplementing an embodiment. In the illustrated embodiment, distributedsystem 1500 includes one or more client computing devices 1502, 1504,1506, and 1508, which are configured to execute and operate a clientapplication such as a web browser, proprietary client (e.g., OracleForms), or the like over one or more network(s) 1510. Server 1512 may becommunicatively coupled with remote client computing devices 1502, 1504,1506, and 1508 via network 1510.

In various embodiments, server 1512 may be adapted to run one or moreservices or software applications. In certain embodiments, server 1512may also provide other services or software applications can includenon-virtual and virtual environments. In some embodiments, theseservices may be offered as web-based or cloud services or under aSoftware as a Service (SaaS) model to the users of client computingdevices 1502, 1504, 1506, and/or 1508. Users operating client computingdevices 1502, 1504, 1506, and/or 1508 may in turn utilize one or moreclient applications to interact with server 1512 to utilize the servicesprovided by these components.

In the configuration depicted in FIG. 15, software components 1518, 1520and 1522 of system 1500 are shown as being implemented on server 1512.In other embodiments, one or more of the components of system 1500and/or the services provided by these components may also be implementedby one or more of the client computing devices 1502, 1504, 1506, and/or1508. Users operating the client computing devices may then utilize oneor more client applications to use the services provided by thesecomponents. These components may be implemented in hardware, firmware,software, or combinations thereof. It should be appreciated that variousdifferent system configurations are possible, which may be differentfrom distributed system 1500. The embodiment shown in FIG. 15 is thusone example of a distributed system for implementing an embodimentsystem and is not intended to be limiting.

Client computing devices 1502, 1504, 1506, and/or 1508 may includevarious types of computing systems. For example, a client computingdevice may include portable handheld devices (e.g., an iPhone®, cellulartelephone, an iPad®, computing tablet, a personal digital assistant(PDA)) or wearable devices (e.g., a Google Glass® head mounted display),running software such as Microsoft Windows Mobile®, and/or a variety ofmobile operating systems such as iOS, Windows Phone, Android, BlackBerry10, Palm OS, and the like. The devices may support various applicationssuch as various Internet-related apps, e-mail, short message service(SMS) applications, and may use various other communication protocols.The client computing devices may also include general purpose personalcomputers including, by way of example, personal computers and/or laptopcomputers running various versions of Microsoft Windows®, AppleMacintosh®, and/or Linux operating systems. The client computing devicescan be workstation computers running any of a variety ofcommercially-available UNIX® or UNIX-like operating systems, includingwithout limitation the variety of GNU/Linux operating systems, such asfor example, Google Chrome OS. Client computing devices may also includeelectronic devices such as a thin-client computer, an Internet-enabledgaming system (e.g., a Microsoft Xbox gaming console with or without aKinect® gesture input device), and/or a personal messaging device,capable of communicating over network(s) 1510.

Although distributed system 1500 in FIG. 15 is shown with four clientcomputing devices, any number of client computing devices may besupported. Other devices, such as devices with sensors, etc., mayinteract with server 1512.

Network(s) 1510 in distributed system 1500 may be any type of networkfamiliar to those skilled in the art that can support datacommunications using any of a variety of available protocols, includingwithout limitation TCP/IP (transmission control protocol/Internetprotocol), SNA (systems network architecture), IPX (Internet packetexchange), AppleTalk, and the like. Merely by way of example, network(s)1510 can be a local area network (LAN), networks based on Ethernet,Token-Ring, a wide-area network, the Internet, a virtual network, avirtual private network (VPN), an intranet, an extranet, a publicswitched telephone network (PSTN), an infra-red network, a wirelessnetwork (e.g., a network operating under any of the Institute ofElectrical and Electronics (IEEE) 802.11 suite of protocols, Bluetooth®,and/or any other wireless protocol), and/or any combination of theseand/or other networks.

Server 1512 may be composed of one or more general purpose computers,specialized server computers (including, by way of example, PC (personalcomputer) servers, UNIX® servers, mid-range servers, mainframecomputers, rack-mounted servers, etc.), server farms, server clusters,or any other appropriate arrangement and/or combination. Server 1512 caninclude one or more virtual machines running virtual operating systems,or other computing architectures involving virtualization. One or moreflexible pools of logical storage devices can be virtualized to maintainvirtual storage devices for the server. Virtual networks can becontrolled by server 1512 using software defined networking. In variousembodiments, server 1512 may be adapted to run one or more services orsoftware applications described in the foregoing disclosure. Forexample, server 1512 may correspond to a server for performingprocessing as described above according to an embodiment of the presentdisclosure.

Server 1512 may run an operating system including any of those discussedabove, as well as any commercially available server operating system.Server 1512 may also run any of a variety of additional serverapplications and/or mid-tier applications, including HTTP (hypertexttransport protocol) servers, FTP (file transfer protocol) servers, CGI(common gateway interface) servers, JAVA® servers, database servers, andthe like. Exemplary database servers include without limitation thosecommercially available from Oracle, Microsoft, Sybase, IBM(International Business Machines), and the like.

In some implementations, server 1512 may include one or moreapplications to analyze and consolidate data feeds and/or event updatesreceived from users of client computing devices 1502, 1504, 1506, and1508. As an example, data feeds and/or event updates may include, butare not limited to, Twitter® feeds, Facebook® updates or real-timeupdates received from one or more third party information sources andcontinuous data streams, which may include real-time events related tosensor data applications, financial tickers, network performancemeasuring tools (e.g., network monitoring and traffic managementapplications), clickstream analysis tools, automobile trafficmonitoring, and the like. Server 1512 may also include one or moreapplications to display the data feeds and/or real-time events via oneor more display devices of client computing devices 1502, 1504, 1506,and 1508.

Distributed system 1500 may also include one or more databases 1514 and1516. These databases may provide a mechanism for storing informationsuch as user interactions information, usage patterns information,adaptation rules information, and other information used by embodimentsof the present disclosure. Databases 1514 and 1516 may reside in avariety of locations. By way of example, one or more of databases 1514and 1516 may reside on a non-transitory storage medium local to (and/orresident in) server 1512. Alternatively, databases 1514 and 1516 may beremote from server 1512 and in communication with server 1512 via anetwork-based or dedicated connection. In one set of embodiments,databases 1514 and 1516 may reside in a storage-area network (SAN).Similarly, any necessary files for performing the functions attributedto server 1512 may be stored locally on server 1512 and/or remotely, asappropriate. In one set of embodiments, databases 1514 and 1516 mayinclude relational databases, such as databases provided by Oracle thatare adapted to store, update, and retrieve data in response toSQL-formatted commands.

In some embodiments, a cloud environment may provide one or moreservices. FIG. 16 is a simplified block diagram of one or morecomponents of a system environment 1600 in which services may be offeredas cloud services, in accordance with an embodiment of the presentdisclosure. In the illustrated embodiment in FIG. 16, system environment1600 includes one or more client computing devices 1604, 1606, and 1608that may be used by users to interact with a cloud infrastructure system1602 that provides cloud services. Cloud infrastructure system 1602 maycomprise one or more computers and/or servers that may include thosedescribed above for server 1612.

It should be appreciated that cloud infrastructure system 1602 depictedin FIG. 16 may have other components than those depicted. Further, theembodiment shown in FIG. 16 is only one example of a cloudinfrastructure system that may incorporate an embodiment of the presentdisclosure. In some other embodiments, cloud infrastructure system 1602may have more or fewer components than shown in the figure, may combinetwo or more components, or may have a different configuration orarrangement of components.

Client computing devices 1604, 1606, and 1608 may be devices similar tothose described above. Client computing devices 1604, 1606, and 1608 maybe configured to operate a client application such as a web browser, aproprietary client application (e.g., Oracle Forms), or some otherapplication, which may be used by a user of the client computing deviceto interact with cloud infrastructure system 1602 to use servicesprovided by cloud infrastructure system 1602. Although exemplary systemenvironment 1600 is shown with three client computing devices, anynumber of client computing devices may be supported. Other devices suchas devices with sensors, etc. may interact with cloud infrastructuresystem 1602.

Network(s) 1610 may facilitate communications and exchange of databetween client computing devices 1604, 1606, and 1608 and cloudinfrastructure system 1602. Each network may be any type of networkfamiliar to those skilled in the art that can support datacommunications using any of a variety of commercially-availableprotocols, including those described above for network(s) 1610.

In certain embodiments, services provided by cloud infrastructure system1602 may include a host of services that are made available to users ofthe cloud infrastructure system on demand. Various other services mayalso be offered including without limitation online data storage andbackup solutions, Web-based e-mail services, hosted office suites anddocument collaboration services, database processing, managed technicalsupport services, and the like. Services provided by the cloudinfrastructure system can dynamically scale to meet the needs of itsusers.

In certain embodiments, a specific instantiation of a service providedby cloud infrastructure system 1602 may be referred to herein as a“service instance.” In general, any service made available to a user viaa communication network, such as the Internet, from a cloud serviceprovider's system is referred to as a “cloud service.” Typically, in apublic cloud environment, servers and systems that make up the cloudservice provider's system are different from the customer's ownon-premises servers and systems. For example, a cloud service provider'ssystem may host an application, and a user may, via a communicationnetwork such as the Internet, on demand, order and use the application.

In some examples, a service in a computer network cloud infrastructuremay include protected computer network access to storage, a hosteddatabase, a hosted web server, a software application, or other serviceprovided by a cloud vendor to a user, or as otherwise known in the art.For example, a service can include password-protected access to remotestorage on the cloud through the Internet. As another example, a servicecan include a web service-based hosted relational database and ascript-language middleware engine for private use by a networkeddeveloper. As another example, a service can include access to an emailsoftware application hosted on a cloud vendor's web site.

In certain embodiments, cloud infrastructure system 1602 may include asuite of applications, middleware, and database service offerings thatare delivered to a customer in a self-service, subscription-based,elastically scalable, reliable, highly available, and secure manner. Anexample of such a cloud infrastructure system is the Oracle Public Cloudprovided by the present assignee.

Cloud infrastructure system 1602 may also provide “big data” elatedcomputation and analysis services. The term “big data” is generally usedto refer to extremely large data sets that can be stored and manipulatedby analysts and researchers to visualize large amounts of data, detecttrends, and/or otherwise interact with the data. This big data andrelated applications can be hosted and/or manipulated by aninfrastructure system on many levels and at different scales. Tens,hundreds, or thousands of processors linked in parallel can act uponsuch data in order to present it or simulate external forces on the dataor what it represents. These data sets can involve structured data, suchas that organized in a database or otherwise according to a structuredmodel, and/or unstructured data (e.g., emails, images, data blobs(binary large objects), web pages, complex event processing). Byleveraging an ability of an embodiment to relatively quickly focus more(or fewer) computing resources upon an objective, the cloudinfrastructure system may be better available to carry out tasks onlarge data sets based on demand from a business, government agency,research organization, private individual, group of like-mindedindividuals or organizations, or other entity.

In various embodiments, cloud infrastructure system 1602 may be adaptedto automatically provision, manage and track a customer's subscriptionto services offered by cloud infrastructure system 1602. Cloudinfrastructure system 1602 may provide the cloud services via differentdeployment models. For example, services may be provided under a publiccloud model in which cloud infrastructure system 1602 is owned by anorganization selling cloud services (e.g., owned by Oracle Corporation)and the services are made available to the general public or differentindustry enterprises. As another example, services may be provided undera private cloud model in which cloud infrastructure system 1602 isoperated solely for a single organization and may provide services forone or more entities within the organization. The cloud services mayalso be provided under a community cloud model in which cloudinfrastructure system 1602 and the services provided by cloudinfrastructure system 1602 are shared by several organizations in arelated community. The cloud services may also be provided under ahybrid cloud model, which is a combination of two or more differentmodels.

In some embodiments, the services provided by cloud infrastructuresystem 1602 may include one or more services provided under Software asa Service (SaaS) category, Platform as a Service (PaaS) category,Infrastructure as a Service (IaaS) category, or other categories ofservices including hybrid services. A customer, via a subscriptionorder, may order one or more services provided by cloud infrastructuresystem 1602. Cloud infrastructure system 1602 then performs processingto provide the services in the customer's subscription order.

In some embodiments, the services provided by cloud infrastructuresystem 1602 may include, without limitation, application services,platform services and infrastructure services. In some examples,application services may be provided by the cloud infrastructure systemvia a SaaS platform. The SaaS platform may be configured to providecloud services that fall under the SaaS category. For example, the SaaSplatform may provide capabilities to build and deliver a suite ofon-demand applications on an integrated development and deploymentplatform. The SaaS platform may manage and control the underlyingsoftware and infrastructure for providing the SaaS services. Byutilizing the services provided by the SaaS platform, customers canutilize applications executing on the cloud infrastructure system.Customers can acquire the application services without the need forcustomers to purchase separate licenses and support. Various differentSaaS services may be provided. Examples include, without limitation,services that provide solutions for sales performance management,enterprise integration, and business flexibility for largeorganizations.

In some embodiments, platform services may be provided by cloudinfrastructure system 1602 via a PaaS platform. The PaaS platform may beconfigured to provide cloud services that fall under the PaaS category.Examples of platform services may include without limitation servicesthat enable organizations (such as Oracle) to consolidate existingapplications on a shared, common architecture, as well as the ability tobuild new applications that leverage the shared services provided by theplatform. The PaaS platform may manage and control the underlyingsoftware and infrastructure for providing the PaaS services. Customerscan acquire the PaaS services provided by cloud infrastructure system1602 without the need for customers to purchase separate licenses andsupport. Examples of platform services include, without limitation,Oracle Java Cloud Service (JCS), Oracle Database Cloud Service (DBCS),and others.

By utilizing the services provided by the PaaS platform, customers canemploy programming languages and tools supported by the cloudinfrastructure system and also control the deployed services. In someembodiments, platform services provided by the cloud infrastructuresystem may include database cloud services, middleware cloud services(e.g., Oracle Fusion Middleware services), and Java cloud services. Inone embodiment, database cloud services may support shared servicedeployment models that enable organizations to pool database resourcesand offer customers a Database as a Service in the form of a databasecloud. Middleware cloud services may provide a platform for customers todevelop and deploy various business applications, and Java cloudservices may provide a platform for customers to deploy Javaapplications, in the cloud infrastructure system.

Various different infrastructure services may be provided by an IaaSplatform in the cloud infrastructure system. The infrastructure servicesfacilitate the management and control of the underlying computingresources, such as storage, networks, and other fundamental computingresources for customers utilizing services provided by the SaaS platformand the PaaS platform.

In certain embodiments, cloud infrastructure system 1602 may alsoinclude infrastructure resources 1630 for providing the resources usedto provide various services to customers of the cloud infrastructuresystem. In one embodiment, infrastructure resources 1630 may includepre-integrated and optimized combinations of hardware, such as servers,storage, and networking resources to execute the services provided bythe PaaS platform and the SaaS platform, and other resources.

In some embodiments, resources in cloud infrastructure system 1602 maybe shared by multiple users and dynamically re-allocated per demand.Additionally, resources may be allocated to users in different timezones. For example, cloud infrastructure system 1602 may enable a firstset of users in a first time zone to utilize resources of the cloudinfrastructure system for a specified number of hours and then enablethe re-allocation of the same resources to another set of users locatedin a different time zone, thereby maximizing the utilization ofresources.

In certain embodiments, a number of internal shared services 1632 may beprovided that are shared by different components or modules of cloudinfrastructure system 1602 to enable provision of services by cloudinfrastructure system 1602. These internal shared services may include,without limitation, a security and identity service, an integrationservice, an enterprise repository service, an enterprise managerservice, a virus scanning and white list service, a high availability,backup and recovery service, service for enabling cloud support, anemail service, a notification service, a file transfer service, and thelike.

In certain embodiments, cloud infrastructure system 1602 may providecomprehensive management of cloud services (e.g., SaaS, PaaS, and IaaSservices) in the cloud infrastructure system. In one embodiment, cloudmanagement functionality may include capabilities for provisioning,managing and tracking a customer's subscription received by cloudinfrastructure system 1602, and the like.

In one embodiment, as depicted in FIG. 16, cloud managementfunctionality may be provided by one or more modules, such as an ordermanagement module 1620, an order orchestration module 1622, an orderprovisioning module 1624, an order management and monitoring module1626, and an identity management module 1628. These modules may includeor be provided using one or more computers and/or servers, which may begeneral purpose computers, specialized server computers, server farms,server clusters, or any other appropriate arrangement and/orcombination.

In an exemplary operation, at step 1634, a customer using a clientdevice, such as client computing devices 1604, 1606 or 1608, mayinteract with cloud infrastructure system 1602 by requesting one or moreservices provided by cloud infrastructure system 1602 and placing anorder for a subscription for one or more services offered by cloudinfrastructure system 1602. In certain embodiments, the customer mayaccess a cloud User Interface (UI) such as cloud UI 1612, cloud UI 1614and/or cloud UI 1616 and place a subscription order via these UIs. Theorder information received by cloud infrastructure system 1602 inresponse to the customer placing an order may include informationidentifying the customer and one or more services offered by the cloudinfrastructure system 1602 that the customer intends to subscribe to.

At step 1636, the order information received from the customer may bestored in an order database 1618. If this is a new order, a new recordmay be created for the order. In one embodiment, order database 1618 canbe one of several databases operated by cloud infrastructure system 1618and operated in conjunction with other system elements.

At step 1638, the order information may be forwarded to an ordermanagement module 1620 that may be configured to perform billing andaccounting functions related to the order, such as verifying the order,and upon verification, booking the order.

At step 1640, information regarding the order may be communicated to anorder orchestration module 1622 that is configured to orchestrate theprovisioning of services and resources for the order placed by thecustomer. In some instances, order orchestration module 1622 may use theservices of order provisioning module 1624 for the provisioning. Incertain embodiments, order orchestration module 1622 enables themanagement of business processes associated with each order and appliesbusiness logic to determine whether an order should proceed toprovisioning.

As shown in the embodiment depicted in FIG. 16, at step 1642, uponreceiving an order for a new subscription, order orchestration module1622 sends a request to order provisioning module 1624 to allocateresources and configure resources needed to fulfill the subscriptionorder. Order provisioning module 1624 enables the allocation ofresources for the services ordered by the customer. Order provisioningmodule 1624 provides a level of abstraction between the cloud servicesprovided by cloud infrastructure system 1600 and the physicalimplementation layer that is used to provision the resources forproviding the requested services. This enables order orchestrationmodule 1622 to be isolated from implementation details, such as whetheror not services and resources are actually provisioned on the fly orpre-provisioned and only allocated/assigned upon request.

At step 1644, once the services and resources are provisioned, anotification may be sent to the subscribing customers indicating thatthe requested service is now ready for use. In some instance,information (e.g. a link) may be sent to the customer that enables thecustomer to start using the requested services.

At step 1646, a customer's subscription order may be managed and trackedby an order management and monitoring module 1626. In some instances,order management and monitoring module 1626 may be configured to collectusage statistics regarding a customer use of subscribed services. Forexample, statistics may be collected for the amount of storage used, theamount data transferred, the number of users, and the amount of systemup time and system down time, and the like.

In certain embodiments, cloud infrastructure system 1600 may include anidentity management module 1628 that is configured to provide identityservices, such as access management and authorization services in cloudinfrastructure system 1600. In some embodiments, identity managementmodule 1628 may control information about customers who wish to utilizethe services provided by cloud infrastructure system 1602. Suchinformation can include information that authenticates the identities ofsuch customers and information that describes which actions thosecustomers are authorized to perform relative to various system resources(e.g., files, directories, applications, communication ports, memorysegments, etc.) Identity management module 1628 may also include themanagement of descriptive information about each customer and about howand by whom that descriptive information can be accessed and modified.

FIG. 17 illustrates an exemplary computer system 1700 that may be usedto implement an embodiment of the present disclosure. In someembodiments, computer system 1700 may be used to implement any of thevarious servers and computer systems described above. As shown in FIG.17, computer system 1700 includes various subsystems including aprocessing unit 1704 that communicates with a number of peripheralsubsystems via a bus subsystem 1702. These peripheral subsystems mayinclude a processing acceleration unit 1706, an I/O subsystem 1708, astorage subsystem 1718 and a communications subsystem 1724. Storagesubsystem 1718 may include tangible computer-readable storage media 1722and a system memory 1710.

Bus subsystem 1702 provides a mechanism for letting the variouscomponents and subsystems of computer system 1700 communicate with eachother as intended. Although bus subsystem 1702 is shown schematically asa single bus, alternative embodiments of the bus subsystem may utilizemultiple buses. Bus subsystem 1702 may be any of several types of busstructures including a memory bus or memory controller, a peripheralbus, and a local bus using any of a variety of bus architectures. Forexample, such architectures may include an Industry StandardArchitecture (ISA) bus, Micro Channel Architecture (MCA) bus, EnhancedISA (EISA) bus, Video Electronics Standards Association (VESA) localbus, and Peripheral Component Interconnect (PCI) bus, which can beimplemented as a Mezzanine bus manufactured to the IEEE P1386.1standard, and the like.

Processing subsystem 1704 controls the operation of computer system 1700and may comprise one or more processing units 1732, 1734, etc. Aprocessing unit may include be one or more processors, including singlecore or multicore processors, one or more cores of processors, orcombinations thereof. In some embodiments, processing subsystem 1704 caninclude one or more special purpose co-processors such as graphicsprocessors, digital signal processors (DSPs), or the like. In someembodiments, some or all of the processing units of processing subsystem1704 can be implemented using customized circuits, such as applicationspecific integrated circuits (ASICs), or field programmable gate arrays(FPGAs).

In some embodiments, the processing units in processing subsystem 1704can execute instructions stored in system memory 1710 or on computerreadable storage media 1722. In various embodiments, the processingunits can execute a variety of programs or code instructions and canmaintain multiple concurrently executing programs or processes. At anygiven time, some or all of the program code to be executed can beresident in system memory 1710 and/or on computer-readable storage media1722 including potentially on one or more storage devices. Throughsuitable programming, processing subsystem 1704 can provide variousfunctionalities.

In certain embodiments, a processing acceleration unit 1706 may beprovided for performing customized processing or for off-loading some ofthe processing performed by processing subsystem 1704 so as toaccelerate the overall processing performed by computer system 1700.

I/O subsystem 1708 may include devices and mechanisms for inputtinginformation to computer system 1700 and/or for outputting informationfrom or via computer system 1700. In general, use of the term “inputdevice” is intended to include all possible types of devices andmechanisms for inputting information to computer system 1700. Userinterface input devices may include, for example, a keyboard, pointingdevices such as a mouse or trackball, a touchpad or touch screenincorporated into a display, a scroll wheel, a click wheel, a dial, abutton, a switch, a keypad, audio input devices with voice commandrecognition systems, microphones, and other types of input devices. Userinterface input devices may also include motion sensing and/or gesturerecognition devices such as the Microsoft Kinect® motion sensor thatenables users to control and interact with an input device, theMicrosoft Xbox® 360 game controller, devices that provide an interfacefor receiving input using gestures and spoken commands. User interfaceinput devices may also include eye gesture recognition devices such asthe Google Glass® blink detector that detects eye activity (e.g.,“blinking” while taking pictures and/or making a menu selection) fromusers and transforms the eye gestures as input into an input device(e.g., Google Glass®). Additionally, user interface input devices mayinclude voice recognition sensing devices that enable users to interactwith voice recognition systems (e.g., Siri® navigator), through voicecommands.

Other examples of user interface input devices include, withoutlimitation, three dimensional (3D) mice, joysticks or pointing sticks,gamepads and graphic tablets, and audio/visual devices such as speakers,digital cameras, digital camcorders, portable media players, webcams,image scanners, fingerprint scanners, barcode reader 3D scanners, 3Dprinters, laser rangefinders, and eye gaze tracking devices.Additionally, user interface input devices may include, for example,medical imaging input devices such as computed tomography, magneticresonance imaging, position emission tomography, medical ultrasonographydevices. User interface input devices may also include, for example,audio input devices such as MIDI keyboards, digital musical instrumentsand the like.

User interface output devices may include a display subsystem, indicatorlights, or non-visual displays such as audio output devices, etc. Thedisplay subsystem may be a cathode ray tube (CRT), a flat-panel device,such as that using a liquid crystal display (LCD) or plasma display, aprojection device, a touch screen, and the like. In general, use of theterm “output device” is intended to include all possible types ofdevices and mechanisms for outputting information from computer system1700 to a user or other computer. For example, user interface outputdevices may include, without limitation, a variety of display devicesthat visually convey text, graphics and audio/video information such asmonitors, printers, speakers, headphones, automotive navigation systems,plotters, voice output devices, and modems.

Storage subsystem 1718 provides a repository or data store for storinginformation that is used by computer system 1700. Storage subsystem 1718provides a tangible non-transitory computer-readable storage medium forstoring the basic programming and data constructs that provide thefunctionality of some embodiments. Software (programs, code modules,instructions) that when executed by processing subsystem 1704 providethe functionality described above may be stored in storage subsystem1718. The software may be executed by one or more processing units ofprocessing subsystem 1704. Storage subsystem 1718 may also provide arepository for storing data used in accordance with the presentdisclosure.

Storage subsystem 1718 may include one or more non-transitory memorydevices, including volatile and non-volatile memory devices. As shown inFIG. 17, storage subsystem 1718 includes a system memory 1710 and acomputer-readable storage media 1722. System memory 1710 may include anumber of memories including a volatile main random access memory (RAM)for storage of instructions and data during program execution and anon-volatile read only memory (ROM) or flash memory in which fixedinstructions are stored. In some implementations, a basic input/outputsystem (BIOS), containing the basic routines that help to transferinformation between elements within computer system 1700, such as duringstart-up, may typically be stored in the ROM. The RAM typically containsdata and/or program modules that are presently being operated andexecuted by processing subsystem 1704. In some implementations, systemmemory 1710 may include multiple different types of memory, such asstatic random access memory (SRAM) or dynamic random access memory(DRAM).

By way of example, and not limitation, as depicted in FIG. 17, systemmemory 1710 may store application programs 1712, which may includeclient applications, Web browsers, mid-tier applications, relationaldatabase management systems (RDBMS), etc., program data 1714, and anoperating system 1716. By way of example, operating system 1716 mayinclude various versions of Microsoft Windows®, Apple Macintosh®, and/orLinux operating systems, a variety of commercially-available UNIX® orUNIX-like operating systems (including without limitation the variety ofGNU/Linux operating systems, the Google Chrome® OS, and the like) and/ormobile operating systems such as iOS, Windows® Phone, Android® OS,BlackBerry® 10 OS, and Palm® OS operating systems.

Computer-readable storage media 1722 may store programming and dataconstructs that provide the functionality of some embodiments. Software(programs, code modules, instructions) that when executed by processingsubsystem 1704 a processor provide the functionality described above maybe stored in storage subsystem 1718. By way of example,computer-readable storage media 1722 may include non-volatile memorysuch as a hard disk drive, a magnetic disk drive, an optical disk drivesuch as a CD ROM, DVD, a Blu-Ray® disk, or other optical media.Computer-readable storage media 1722 may include, but is not limited to,Zip® drives, flash memory cards, universal serial bus (USB) flashdrives, secure digital (SD) cards, DVD disks, digital video tape, andthe like. Computer-readable storage media 1722 may also include,solid-state drives (SSD) based on non-volatile memory such asflash-memory based SSDs, enterprise flash drives, solid state ROM, andthe like, SSDs based on volatile memory such as solid state RAM, dynamicRAM, static RAM, DRAM-based SSDs, magnetoresistive RAM (MRAM) SSDs, andhybrid SSDs that use a combination of DRAM and flash memory based SSDs.Computer-readable media 1722 may provide storage of computer-readableinstructions, data structures, program modules, and other data forcomputer system 1700.

In certain embodiments, storage subsystem 1700 may also include acomputer-readable storage media reader 1720 that can further beconnected to computer-readable storage media 1722. Together and,optionally, in combination with system memory 1710, computer-readablestorage media 1722 may comprehensively represent remote, local, fixed,and/or removable storage devices plus storage media for storingcomputer-readable information.

In certain embodiments, computer system 1700 may provide support forexecuting one or more virtual machines. Computer system 1700 may executea program such as a hypervisor for facilitating the configuring andmanaging of the virtual machines. Each virtual machine may be allocatedmemory, compute (e.g., processors, cores), I/O, and networkingresources. Each virtual machine typically runs its own operating system,which may be the same as or different from the operating systemsexecuted by other virtual machines executed by computer system 1700.Accordingly, multiple operating systems may potentially be runconcurrently by computer system 1700. Each virtual machine generallyruns independently of the other virtual machines.

Communications subsystem 1724 provides an interface to other computersystems and networks. Communications subsystem 1724 serves as aninterface for receiving data from and transmitting data to other systemsfrom computer system 1700. For example, communications subsystem 1724may enable computer system 1700 to establish a communication channel toone or more client computing devices via the Internet for receiving andsending information from and to the client computing devices.

Communication subsystem 1724 may support both wired and/or wirelesscommunication protocols. For example, in certain embodiments,communications subsystem 1724 may include radio frequency (RF)transceiver components for accessing wireless voice and/or data networks(e.g., using cellular telephone technology, advanced data networktechnology, such as 3G, 4G or EDGE (enhanced data rates for globalevolution), WiFi (IEEE 802.11 family standards, or other mobilecommunication technologies, or any combination thereof), globalpositioning system (GPS) receiver components, and/or other components.In some embodiments communications subsystem 1724 can provide wirednetwork connectivity (e.g., Ethernet) in addition to or instead of awireless interface.

Communication subsystem 1724 can receive and transmit data in variousforms. For example, in some embodiments, communications subsystem 1724may receive input communication in the form of structured and/orunstructured data feeds 1726, event streams 1728, event updates 1730,and the like. For example, communications subsystem 1724 may beconfigured to receive (or send) data feeds 1726 in real-time from usersof social media networks and/or other communication services such asTwitter® feeds, Facebook® updates, web feeds such as Rich Site Summary(RSS) feeds, and/or real-time updates from one or more third partyinformation sources.

In certain embodiments, communications subsystem 1724 may be configuredto receive data in the form of continuous data streams, which mayinclude event streams 1728 of real-time events and/or event updates1730, that may be continuous or unbounded in nature with no explicitend. Examples of applications that generate continuous data may include,for example, sensor data applications, financial tickers, networkperformance measuring tools (e.g. network monitoring and trafficmanagement applications), clickstream analysis tools, automobile trafficmonitoring, and the like.

Communications subsystem 1724 may also be configured to output thestructured and/or unstructured data feeds 1726, event streams 1728,event updates 1730, and the like to one or more databases that may be incommunication with one or more streaming data source computers coupledto computer system 1700.

Computer system 1700 can be one of various types, including a handheldportable device (e.g., an iPhone® cellular phone, an iPad® computingtablet, a PDA), a wearable device (e.g., a Google Glass® head mounteddisplay), a personal computer, a workstation, a mainframe, a kiosk, aserver rack, or any other data processing system.

Due to the ever-changing nature of computers and networks, thedescription of computer system 1700 depicted in FIG. 17 is intended onlyas a specific example. Many other configurations having more or fewercomponents than the system depicted in FIG. 17 are possible. Based onthe disclosure and teachings provided herein, a person of ordinary skillin the art will appreciate other ways and/or methods to implement thevarious embodiments.

Although specific embodiments of the present disclosure have beendescribed, various modifications, alterations, alternativeconstructions, and equivalents are also encompassed within the scope ofthe present disclosure. The modifications include any relevantcombination of the disclosed features. Embodiments of the presentdisclosure are not restricted to operation within certain specific dataprocessing environments, but are free to operate within a plurality ofdata processing environments. Additionally, although embodiments of thepresent disclosure have been described using a particular series oftransactions and steps, it should be apparent to those skilled in theart that the scope of the present disclosure is not limited to thedescribed series of transactions and steps. Various features and aspectsof the above-described embodiments may be used individually or jointly.

Further, while embodiments of the present disclosure have been describedusing a particular combination of hardware and software, it should berecognized that other combinations of hardware and software are alsowithin the scope of the present disclosure. Embodiments of the presentdisclosure may be implemented only in hardware, or only in software, orusing combinations thereof. The various processes described herein canbe implemented on the same processor or different processors in anycombination. Accordingly, where components or modules are described asbeing configured to perform certain operations, such configuration canbe accomplished, e.g., by designing electronic circuits to perform theoperation, by programming programmable electronic circuits (such asmicroprocessors) to perform the operation, or any combination thereof.Processes can communicate using a variety of techniques including butnot limited to conventional techniques for interprocess communication,and different pairs of processes may use different techniques, or thesame pair of processes may use different techniques at different times.

The specification and drawings are, accordingly, to be regarded in anillustrative rather than a restrictive sense. It will, however, beevident that additions, subtractions, deletions, and other modificationsand changes may be made thereunto without departing from the broaderspirit and scope as set forth in the claims. Thus, although specificembodiments have been described, these are not intended to be limiting.Various modifications and equivalents are within the scope of thefollowing claims.

What is claimed is:
 1. A computer-implemented method, the method beingperformed by one or more computer systems and comprising: determiningheap information of one or more processes during a length of time, theheap information comprising heap usage information and a smoothed heapusage seasonal factor for a season of each of a plurality of intervalsin the length of time; determining thread information of the one or moreprocesses during the length of time, wherein the thread informationcomprises a smoothed thread intensity seasonal factor for a season ofeach of the plurality of intervals in the length of time; correlatingthe heap information with the thread information to identify one or morelines of code of the one or more processes that correspond to the heapusage exceeding a threshold; and responsive to identifying the one ormore lines of code, initiating one or more actions associated with theone or more lines of code.
 2. The method of claim 1, wherein the lengthof time corresponds to when heap usage by the one or more processesexceeds the threshold, the heap usage being represented by the heapusage information.
 3. The method of claim 2, wherein the threshold isbased at least in part on a pre-determined percentage of a range of aheap usage seasonal factor for the each of the plurality of intervals.4. The method of claim 2, wherein the heap usage corresponds to anamount of heap memory used by the one or more processes during thelength of time.
 5. The method of claim 1, where: the length of timespans a first period having a first length and a second period having asecond length; the first period having the first length is divided intoa first plurality of seasons each associated with the smoothed heapusage seasonal factor of a first type and the smoothed thread intensityseasonal factor of a first type; the second period having the secondlength is divided into a second plurality of seasons each associatedwith the smoothed heap usage seasonal factor of a second type and thesmoothed thread intensity seasonal factor of a second type; each of theplurality of intervals is mapped to one of the first plurality ofseasons or one of the second plurality of seasons; for each of theplurality of intervals, the smoothed heap usage seasonal factor isassociated with the one of the first plurality of seasons or the one ofthe second plurality of seasons that the interval is mapped to; and foreach of the plurality of intervals, the smoothed thread intensityseasonal factor is associated with the one of the first plurality ofseasons or the one of the second plurality of seasons that the intervalis mapped to.
 6. The method of claim 5, wherein the smoothed heap usageseasonal factors of the first type are determined based at least in parton: for each of the first plurality of seasons, determining a heap usageseasonal factor of the first type based at least in part on an averageheap usage of the season of the first plurality of seasons and anaverage heap usage of the period having the first length; and obtainingthe smoothed heap usage seasonal factors of the first type based atleast in part on a the heap usage seasonal factors of the first type,and a first spline function; and wherein the smoothed heap usageseasonal factors of the second type are determined based at least inpart on: for each of the second plurality of seasons, determining a heapusage seasonal factor of the second type at least in part on an averageheap usage of the season of the second plurality of seasons and anaverage heap usage of the period having the second length; and obtainingthe smoothed heap usage seasonal factors of the second type based atleast in part on a the heap usage seasonal factors of the second type,and a second spline function.
 7. The method of claim 5, wherein: thesecond period immediately follows the first period; the first period isassociated with a plurality of first heap usage seasonal factors and aplurality of first thread intensity seasonal factors; the second periodis associated with a plurality of second heap usage seasonal factors anda plurality of second thread intensity seasonal factors; the methodfurther comprises: forming a sequence of heap usage seasonal factorsbased at least in part on concatenating the first plurality of heapusage seasonal factors and the second plurality of heap usage seasonalfactors; forming a sequence of thread intensity seasonal factors basedat least in part on concatenating the first plurality of threadintensity seasonal factors and the second plurality of thread intensityseasonal factors; performing a first smooth-spline fitting on thesequence of heap usage seasonal factors to generate a sequence ofsmoothed heap usage seasonal factors to be included in the heapinformation; and performing a second smooth-spline fitting on thesequence of thread intensity seasonal factors to generate a sequence ofsmoothed thread intensity seasonal factors to be included in the threadinformation; and the correlation of the heap information with the threadinformation is based at least in part on the sequence of smoothed heapusage seasonal factors and the sequence of smoothed thread intensityseasonal factors.
 8. The method of claim 7, wherein the first period isassociated with a weekday, and wherein the second period is associatedwith at least one of: a weekend, or a holiday.
 9. The method of claim 1,wherein determining the thread information comprises determining one ormore classes of threads and wherein the thread information comprises,for each of the one or more classes of threads, thread intensityinformation and the thread intensity seasonal factor for each of theplurality of intervals.
 10. The method of claim 9, wherein correlatingthe heap information with the thread information comprises: for each ofthe one or more classes of threads, determining, based at least in parton the smoothed heap usage seasonal factors of the plurality ofintervals and the smoothed thread intensity seasonal factors of theclass of threads and the plurality of intervals, a degree of correlationbetween the class of threads and heap usage by the one or moreprocesses; ranking the one or more classes of threads based at least inpart of the degrees of correlations; selecting a class of threads basedat least in part on the ranking; and identifying, based at least in parton the selected class of threads, the one or more lines of code.
 11. Themethod of claim 10, wherein the degree of correlation between the classof threads and heap usage by the one or more processes is determinedbased at least in part of a mean and a variance of, respectively, thesmoothed heap usage seasonal factors and the smoothed thread intensityseasonal factors of each of the plurality of intervals in the length oftime.
 12. The method of claim 9, wherein determining the one or moreclasses of threads comprises: obtaining one or more thread dumps of theone or more processes, wherein each of the thread dumps corresponds todifferent times; and for each of one or more threads of the one or morethread dumps, classifying the thread based at least in part on a stacktrace that corresponds to the thread, the stack trace indicating a codeexecuted by the thread when the thread dump was taken.
 13. The method ofclaim 12, wherein classifying the thread based at least in part on thestack trace comprises: determining whether a first class of threads thatcorresponds to a combination of stack frames included in the stack traceexists; based on whether the class of threads that corresponds to acombination of stack frames included in the stack trace exists,performing one of: creating a second class of threads that correspondsto the combination of stack frames included in the stack trace, orclassifying the thread into the first class of threads.
 14. The methodof claim 1, wherein the one or more actions includes at least one of:generating an alert associated with the one or more lines of code; oroptimizing the one or more lines of code based at least in part onmodifying the one or more lines of code to reduce an amount of heapmemory used or reduce a duration of a usage of the heap memory.
 15. Asystem comprising: one or more processors; and a memory accessible tothe one or more processors, the memory storing one or more instructionsthat, upon execution by the one or more processors, causes the one ormore processors to: determine heap information of one or more processesduring a length of time, the heap information comprising heap usageinformation and a smoothed heap usage seasonal factor for a season ofeach of a plurality of intervals in the length of time; determine threadinformation of the one or more processes during the length of time,wherein the thread information comprises a smoothed thread intensityseasonal factor for a season of each of the plurality of intervals inthe length of time; correlate the heap information with the threadinformation to identify one or more lines of code of the one or moreprocesses that correspond to the heap usage exceeding a threshold; andresponsive to identifying the one or more lines of code, initiate one ormore actions associated with the one or more lines of code.
 16. Thesystem of claim 15, wherein: the length of time spans a first periodhaving a first length and a second period having a second length; thefirst period having the first length is divided into a first pluralityof seasons each associated with the smoothed heap usage seasonal factorof a first type and the smoothed thread intensity seasonal factor of afirst type; the second period having the second length is divided into asecond plurality of seasons each associated with the smoothed heap usageseasonal factor of a second type and the smoothed thread intensityseasonal factor of a second type; each of the plurality of intervals ismapped to one of the first plurality of seasons or one of the secondplurality of seasons; for each of the plurality of intervals, thesmoothed heap usage seasonal factor is associated with the one of thefirst plurality of seasons or the one of the second plurality of seasonsthat the interval is mapped to; and for each of the plurality ofintervals, the smoothed thread intensity seasonal factor is associatedwith the one of the first plurality of seasons or the one of the secondplurality of seasons that the interval is mapped to.
 17. The system ofclaim 16, wherein the memory further stores one or more instructionsthat, upon execution by the one or more processors, causes the one ormore processors to: determine the smoothed heap usage seasonal factorsof the first type based at least in part on: for each of the firstplurality of seasons, determining a heap usage seasonal factor of thefirst type based at least in part on an average heap usage of the seasonof the first plurality of seasons and an average heap usage of theperiod having the first length; and obtaining the smoothed heap usageseasonal factors of the first type based at least in part on a the heapusage seasonal factors of the first type, and a first spline function;and determine the smoothed heap usage seasonal factors of the secondtype based at least in part on: for each of the second plurality ofseasons, determining a heap usage seasonal factor of the second type atleast in part on an average heap usage of the season of the secondplurality of seasons and an average heap usage of the period having thesecond length; and obtaining the smoothed heap usage seasonal factors ofthe second type based at least in part on a the heap usage seasonalfactors of the second type, and a second spline function.
 18. The systemof claim 16, wherein: the second period immediately follows the firstperiod; the first period is associated with a plurality of first heapusage seasonal factors and a plurality of first thread intensityseasonal factors; the second period is associated with a plurality ofsecond heap usage seasonal factors and a plurality of second threadintensity seasonal factors; wherein the memory further stores one ormore instructions that, upon execution by the one or more processors,causes the one or more processors to: form a sequence of heap usageseasonal factors based at least in part on concatenating the firstplurality of heap usage seasonal factors and the second plurality ofheap usage seasonal factors; form a sequence of thread intensityseasonal factors based at least in part on concatenating the firstplurality of thread intensity seasonal factors and the second pluralityof thread intensity seasonal factors; perform a first smooth-splinefitting on the sequence of heap usage seasonal factors to generate asequence of smoothed heap usage seasonal factors to be included in theheap information; and perform a second smooth-spline fitting on thesequence of thread intensity seasonal factors to generate a sequence ofsmoothed thread intensity seasonal factors to be included in the threadinformation; and the correlation of the heap information with the threadinformation is based at least in part on the sequence of smoothed heapusage seasonal factors and the sequence of smoothed thread intensityseasonal factors.
 19. The system of claim 15, wherein the memory furtherstores one or more instructions that, upon execution by the one or moreprocessors, causes the one or more processors to correlate the heapinformation with the thread information based at least in part on:determining one or more classes of threads, wherein the threadinformation comprises, for each of the one or more classes of threads,thread intensity information and the thread intensity seasonal factorfor each of the plurality of intervals; for each of the one or moreclasses of threads, determining, based at least in part on the smoothedheap usage seasonal factors of the plurality of intervals and thesmoothed thread intensity seasonal factors of the class of threads andthe plurality of intervals, a degree of correlation between the class ofthreads and heap usage by the one or more processes; ranking the one ormore classes of threads based at least in part of the degrees ofcorrelations; selecting a class of threads based at least in part on theranking; and identifying, based at least in part on the selected classof threads, the one or more lines of code.
 20. A non-transitorycomputer-readable medium storing one or more instructions that, uponexecution by one or more processors, cause the one or more processorsto: determine heap information of one or more processes during a lengthof time, the heap information comprising heap usage information and asmoothed heap usage seasonal factor for a season of each of a pluralityof intervals in the length of time; determine thread information of theone or more processes during the length of time, wherein the threadinformation comprises a smoothed thread intensity seasonal factor for aseason of each of the plurality of intervals in the length of time;correlate the heap information with the thread information to identifyone or more lines of code of the one or more processes that correspondto the heap usage exceeding a threshold; and responsive to identifyingthe one or more lines of code, initiate one or more actions associatedwith the one or more lines of code.